Itinerary advice with 1 year old

Will this be your daughter's first plane trip?

Yes. She's very wiggly so I'm nervous about that. She has two speeds- full speed and sleeping. I plan to find a playground in Dublin near wherever our hotel is and set her loose on it for a while on the day we spend getting over jet lag. Car rides I'm not as worried about, as most of them will be planned for when she is napping to get from destination to destination.

You can't see the Cliffs of Moher from the Aran Islands. You could see them en route, perhaps, but it would be better to go there so you could see the visitor center.

Blarney to Cork is over a three hour drive if that gives you any guidance. Driving there can be much slower than the distance might indicate. You are also going to want to stop for pictures, lunch, letting the baby out of her car seat, and whatever else. If I chose something to skip, it would be the Aran Islands. It would be an all-day process (how does she handle traveling in a small boat?), and it is sometimes not possible to travel there if weather or rough water prohibits sailing.

I'm not at all sure how you are figuring your timeframes for the baby's sleep, or how you propose to get her up and put her in the car and have her stay asleep. 7:30 pm in TN is 12:30 am (if you are in the Eastern time zone at home). Having done it, I can guarantee you that she will not sleep a straight 12 hours while you are traveling. Your best bet is not to try to keep her on the home schedule but to get her adjusted to the schedule where you are, just like you will need to do. You will probably just have to play it by ear a bit rather than go with a rigid schedule in mind.

EDIT: Blarney to DOOLIN is over three hours.

The time difference I did calculate incorrectly. I do plan to be flexible, and she usually sleeps well in her car seat. Most of the trips appear to be 3 hours or under with the exception of Doolin to Derry, and I've broken even those into stops at the hallway point. But I totally see that even attempting to keep her on a schedule is probably futile!
The distance from Blarney to Cork is 15 minutes according to Google Maps, so I guess I'm confused when you said it's 3 hours. Did that include the stop at the Castle? I read about cruises from Doolin that go to Inis Oirr and then sail under the Cliffs of Moher on the return. Leave at 10am, 25 minutes to the island, return trip begins at 2 pm, get back at 330, then I thought a cliff top visit would be possible that afternoon. I now see this may get cancelled because of the weather and that's a pretty big concern around the time we're going. Thanks for pointing that out!
Here's my expected travel times:
Dublin to Cork 3 hours (stop halfway at Rock of Cashel for 2 ish hours)
Cork to Doolin (2.5 hour drive)
Doolin to Derry (5 hour drive, but really will be all day for stops etc)
Derry to Giants Causeway (1 hr) to Belfast (1 hr)
Are any of these glaringly wrong? I plan to budget an extra hour in for all of them just for sanity purposes. I really don't want to be so scheduled that we don't have a free minute, but I want to maximize the short time constraints as well.

The only advice I would give with traveling with such a young baby is to be very flexible and go with the flow. Be ok with things taking longer, things being cancelled or things not turning out exactly as you planned.
Bring a few comfort things from home ( favourite blanket, stuffed animal etc), use your car seat on the plane, bring something for her to suck on for take off and landing (helps with ears) and bring any type of medication that you would ever needs/use at home ( tylenol, advil etc)

I mistyped - I meant that Blarney to DOOLIN is three hours (Sept 9). In my experience, www.viamichelin.com is the site to use for estimating times and comparing routes. You need to add maybe 25% to their times, though, to get a more accurate picture. For example, the shortest route they show for Dublin to Cork is 3h14m. With the 25% added, that makes it closer to four hours (though you are on motorway a lot on that particular route, so it might not be so long). And their times include no stops. In areas where you are on smaller roads, it will be slower.

The cruise you mention is the one I was talking about, as well - you see the Cliffs from the boat, not from the island.

Thanks Sharon! I haven't even started a packing list yet, but I would have forgotten the medicines. I'm type A when it comes to the planning, so I can relax and enjoy when I'm there. I know weather is a huge concern. I'm hoping to think and research a million options so I don't waste any time there researching how to reconfigure. When I went to Bolivia 2 years ago, everything went awry but I was able to switch things around and male it work beautifully! Adding a kid to the mix is a definite new challenge though!
And Nancy, thank you so much for the other site. I'll use that to check my map and routes. I'm now thinking of splicing London into the middle of the trip like this:
6- Dublin jet lag
7- Dublin
8- Dublin-> Cashel->Doolin (2 hours, 3 hours driving)
9- Doolin, Cliffs, cruise if we feel like it/weather permits
10- Shannon airport to London
11- London
12- London
13- London-> Derry
14- Derry
15- Derry->Giants Causeway->Belfast (1.5 hours, 1.5 hours driving)
16- Belfast
17- Belfast-> Dublin late afternoon (maybe train?)(3.5 hours driving, could break up with so at Newgrange)
18- Dublin->home

That cuts out Cork and the long drive from Doolin to Derry, and puts the London bustle in the middle instead of at the end. I'm trying to convince him to leave out London or Derry, so we'll see how that goes!

Thanks so much for all the help and advice!