First TIMERS! Just booked our last minute trip to Ireland in Early December

That's a lot for nine days. How are you planning to travel around the country-- car, train, bus?

Regarding the "beer or two", while I don't think you'll have any difficulties finding interesting beer in Dublin, we found elsewhere to be more difficult. When we visited Ireland at the beginning of the month we were based in a town in county Limerick that had 7 or 8 pubs, but all of them offered pretty much the same selection - Guinness, Smithicks (a red ale) and a few lagers.

Outside of that Limerick had a decent "Craft beer pub" in Mother Macs, and a couple of small breweries in Treaty City (near King John's Castle) and Crew (with Taprooms).
If you get to Cork, then they have several places worth visiting - Rising Sons Brewery, the Franciscan Well, the Friary and Bierhaus - the latter had 30 beers on tap, most of them from small Irish breweries.

As foodies, I think we enjoyed the English Market in Cork as a highlight.

Just a reminder, Dublin will have about 7:30 of sunlight in December. Sunset will be just after 4:00 PM. Plan accordingly for driving, sightseeing and outside activities.

All our visits are in the late Spring, so I'm no expert about winter. Music will be once a week in many pubs, except in Dublin, Galway, Doolin, and the like. Your daylight hours are drastically shorter, so you can't hike late in the day or drive long distance without missing interesting things. Our trips tend to be on the "frantic" side, with one-night stops in most places, driving 2-3 hours with rest stops at castles, national parks, etc., so if you're going to relax, don't listen to me! Some people prefer to pick just a few spots and focus, but we love the driving and travel light enough that we never unpack.

My basic strategy is to google "trad music pubs", find a connecting path between them, then search nearby each pub for a B&B within walking distance. (narrow roads and left hand driving are hard enough without alcohol). Visiting each pubs's website or FB page will reveal what nights are good, so juggle the pieces until you get an efficient route. Our first trip just picked equidistant goals, and we got to enjoy very little music (even in early June) because we missed the only night there was music,

Most pubs have a local beer or two, and they all have Guinness, although a few offer another stout in defiance of the monster brewery.

Specifically, if you're doing the ring of Kerry, skip Moher for Cliffs of Kerry. If you're set on Doolin, then maybe skip the Ring and go to Moher. One of our favorite hikes/neolithic things was Carrowkeel. Hiking in gorgeous country is everywhere, so I don't think you'll fail to find good hiking experiences. Just plot your route on Google Maps and look at nearby "attractions" and you'll find castles, standing stones, hiking trails all along each route.

First and last nights should be Dublin so you aren't too jet-lagged to enjoy things and aren't on edge about missing a flight out.

Here's a quick sample of something we would do, removing stops depending on what "9 days" means.
Dublin
Kilkenny Castle, town of
Kilkenny
Rock of Cashel, Cahir Castle
Killarney -or- Kenmare
Killarney NP
(Dingle)
Doolin -or- Ennis
The Burren
Galway
(InishMor day trip or overnight)
Carrowkeel
Carrick-on-Shannon (skippable, but breaks the drive nicely).
NewGrange or Knowth
Dublin

You'll miss all of Connemara, N. Ireland, Wexford. So many places and so little time. It's probably too late to enter the lottery, but if your tri[p overlaps the solstice, try to get to NewGrange or if that fails, any number of other cairn tombs.

How about considering a day trip out to one of the Aran Islands? If you're in the area the Rock of Cashel is worth a couple of hours. My wife and her friend enjoyed the tour of the Waterford Crystal Factory (I stayed in the showroom) but we didn't spend any other time in town. Cliffs of Moher definitely worth a stop - Doolin, Lahinch and Ennis are nearby. Drove through The Burren - beautiful coastal road. Great pubs in Dublin and pretty much everywhere we went. Our trip was only 6 nights and we stayed in Airbnb's 3 nights each (Doolin and Dublin).

To maximize your time and minimize backtracking I suggest that upon arrival in Dublin, you get on the bus to Galway. The bus stop is right outside the terminal and you can pay on the bus or at the kiosk before you board. After you spend your first night or more in Galway, rent a car and start heading south and counterclockwise around the island. You have an ambitious set of stops you want to make and as a PP noted, daylight hours will be limited. It will also be rainy and blustery. If you don't mind hiking in the rain and mud look into the Kerry Way, https://www.kerryway.com. You can pick and choose which hikes you like. Given that December is off season you'll want to make sure that the places you want to see and where you want to stay are open. Return the car in Dublin-probably the airport will be easiest, and don't be tempted to drive in Dublin. Also, don't underestimate drive times. The general rule of thumb is to add 25-30% to whatever drive times the internet gives you. You are unlikely to drive as fast as the posted speed limit. If you are going to drop anything, start with the Waterford Factory. It's the geographic outlier and I was personally underwhelmed by the tour I took 30-odd years ago. And that's when Waterford Crystal was actually made in Ireland.

Are you flying out of Dublin too? It sounds like your heart is set on western Ireland so I suggest flying home from Shannon. Are you comfortable with one-night stays? With only nine nights and a busy itinerary, here’s what I recommend:
Mon – take the bus from Dublin airport to Galway: https://www.dublinairport.com/to-from-the-airport/by-bus/national-coach-services; sleep in Galway.
Tue – pick up rental car and drive to Kylemore Abbey (1h 30m); sleep in Galway.
Wed – drive to the Burren (1h 30m); sleep in Doolin (45-minutes).
Wed – visit the Cliffs of Moher (30-minutes); sleep in Killorglin (2h 45m).
Thu – drive the Ring of Kerry; sleep in Kenmare.
Fri – drive to Kinsale (2h); sleep in Kinsale.
Sat – drive to the Rock of Cashel (2h 30m); sleep in Kilkenny (1h).
Sun – day trip to Waterford Crystal (45-minutes); drop off rental car in Kilkenny and sleep in Kilkenny.
Mon – take a direct bus to Dublin; sleep in Dublin.
Tue – sleep in Dublin.

Just an aside, as it is just one minor point of the OPs questions, but regarding jjgurley's comment "Most pubs have a local beer or two" , this was pretty much the opposite of what we found at the beginning of October this year. It's possible that this was just the areas we were in, but outside of the cities of Limerick and Cork, we found nothing other than mainstream "corporate" beer.

Less is more.

You have a lot of places on your list and you are only going to get 7ish hours of daylight each day MAX. Some days it will hardly get light at all (clouds and rain and such). You dont want to spend your whole vacation in the car driving around, do you? with 9 nights I might say to do 3 stops - maybe 3 nights in Galway, 3 in Killarney and 3 in Dublin? I like the idea of taking the bus to Galway from the airport in Dublin. That way there you arent driving right away, and you could save yourself a day of the rental car costs. Pick a place to stay in Galway and you can see Galway City, Connemara and maybe Cong (I think its a bit ambitious to head to the Aran Islands in December). Then you could drive to Killarney and maybe make a stop at the Cliffs of Moher for a peek. After 3 nights in Killarney, drive to Dublin and drop the car off and spend your last 3 nights in Dublin.

Are you both fully vaccinated? Do you know the current Covid-19 requirements for the Republic of Ireland?

Are you 1st timers for Ireland only or for European travel in general?

Edited to ask: With all the suggestions to rent a car, have you researched the requirements to do that?

My memory of beer offerings may be a bit dated since I switched to Guinness a few trips ago. A remarkable number of younger folks seem to love Bud, Miller Lite, and other barely-beers. Very sad! Guinness is a completely different beer than what you get in the US, IMHO. Of course Guinness is also a mega-corporate producer, too. There are still local whiskeys :-)

Does the 9 nights include your day of arrival? The first day (for me) is always lost to jet lag. As others have mentioned you'll have about 8 hours of daylight to work with, so plan your activities accordingly. Others have mentioned more reasonable itineraries. If you're going to rent a car make the reservation asap, plus I hope you know how to drive a manual transmission (don't assume you will get an automatic). I personally would not attempt driving a car on the opposite side of the road on the day I arrived in Ireland, or honestly, ever! And definitely add 30% to driving times - very few American style highways everything just takes longer (especially if you do either ring road drive).

I haven't been to Ireland in winter, but make sure to pack layers for clothing including a solid waterproof outer layer, hat, and gloves. I was there in mid-May on a tour and had tour mates from Georgia who thought they were going to freeze to death (I'm from Oregon, 50 degrees felt balmy to me).

I've been twice for short trips, once for an Irish Dance Comp for my d when in hs and once for our 25th wedding anniversary. Needless to say, 16 teenaged girls and various mom/dad figures made travel much different from our couples trip.

With the girls in February, we flew in various stages into Dublin for the most part. Rented a car, drove to bnb, walked to bus stop nearby and spent the day in Dublin. We did the hop on-hop off bus, stopped for lunch and Trinity College (Book of Kells an inspiration for Irish dance costume designs), shopping at Avoca (don't miss!) and photo ops. We drove to Killarney the next day for practices, competition, etc. Fit in a bus tour of Ring of Kerry, delightful and would have hated to drive that myself. Also enjoyed Killarney shopping and eating. After comp (they won!), we took a day and drove to Blarney Castle and Kinsale and looped back into original bnb to spend night before leaving. Found the weather temperate. Not always sunny but little rain, often windy but no heavy coats needed, just layers.

Couples trip, we flew into Shannon and home from Dublin so did the "smile". Of course we missed our connection in Chicago and lost a day, so frustrating but actually nice to get to Doolin in morning having paid for the night before just in time for breakfast and a walk around before a nap, then boat along the base of the Cliffs. It was June and daylight until 1030! The next day, we drove up through the Burren, seeing Poulnabroune and sheep herding and down along the coast, cliffs from top, ferry over the river back into Killarney for a couple nights. Walked through the park, hubs golfed Ballybunion and I walked with their group. Drove to Blarney, stayed in Kinsale at Old Head (prob best hotel I've ever stayed in) where hubs golfed again and I spa-dayed it. Drove to Ballymaloe House for best dinner ever after an afternoon in Cobh. Did Jameson tour at some point. Spent two nights in Glendalough and hiked a couple trails. It was warm and barely rained the whole time. We enjoyed driving and stopping when we felt like it-only reservations were for golf and places to stay but it was summer and days were longer.

My son and I traveling in December also. We are staying in Dublin for 3 nights at Clontarf Castle, taking a car from airport that we may barely use but oddly found we couldn't get one for the 2 days we needed it unless booking 5 days. Not feeling too bad about driving it to the Castle with automatic transmission and staying out of the city. We are then driving down the coast to spend night at Killiane Castle outside of Wexford, not sure what we will do along way. Heading to Cork for final night at Montenotte before flying to London the next morning. In Dublin, we will do the bus again on arrival day, Croke Park (son plays Gaelic), Guiness tour/tasting, considering a day trip/drive to either Belfast for Titanic experience (worried about testing requirements in N Ireland for day trip?) or Newgrange instead. I know its going to be cold and possibly wet.