Ireland first time itinerary help/suggestions

Your itinerary looks good. The only change I would make is swapping Doolin (and the Cliffs of Moher) for Killarney. With young kids, my personal opinion is that Doolin and the cliffs area isn't young kid friendly and there isn't as much family-friendly (with young kids) activities in Doolin. Killarney, on the other hand, has loads of stuff for people of all ages to enjoy, especially those with young kiddos.
I would also make sure you visit one of the Sheep herding farms in Dingle (we went to Dingle Sheepdogs.) So fun for the whole family. Have a wonderful trip!

Dingle also has a Falconry Experience that’s great for kids. Frankly, I would also be hesitant about taking 6 & 3 year olds to the Cliffs of Mohr. Our grandkids really enjoyed Killarney with the castle ruins, sheep dog demonstrations, jaunting cart horse drawn rides and short hike back to a waterfall. You might also check further about music as most of the pubs don’t start til 9 and children won’t be allowed. I know we went to a special Trad Session in a Dingle Church one evening. Also, Kyteler’s Inn in Kilkenny had an early Trad session where the kids were welcome. You just need to do a bit of research.

To add: our grandkids enjoyed the playground in St. Stephen’s Green Park, Dublin.

I don't think there is anything in Cobh for young kids, and it doesn't break up the drive because it's so far out of the way. I would consider taking the train to Killarney and renting the car there after you're done with the local activities suggested by the other commenter. Booked ahead, the trains are inexpensive, and the little one will travel for free. Both parents will get to see the scenery from the train. If the little one still naps, maybe try to schedule the train ride for nap time.
I agree that the Cliffs of Moher are not suitable for children.
With just eight days, visiting Dublin, Killarney and Dingle is plenty, especially with little kids in tow. The beaches in and around Dingle are a good choice for kids.

One activity the kids might enjoy (the adults too, come to that) would be a pony trap ride through the Gap of Dunloe near Killarney. It's one of the prettiest little glens in Ireland. Could also walk part of it or maybe rent bikes.
Kate Kearney's cottage near the parking area would be a nice place for lunch or a coffee, and if the little ones can manage it there's a cute little tea room about a mile down the track that serves home made scones.
There are tours based in Killarney that include a crossing of the lake via a small boat, followed by the pony trap thru the Gap and then a bus ride back into town to complete the loop, taking about half a day as I recall.
If you're driving the Ring of Kerry there's a very pretty stretch of sandy beach near the village of Ballinskellings that would be a good place to let them romp. There are the ruins of an old abbey there to explore as well.