We are arriving in Dublin early on the 4th. Staying in Dublin 4&5th. We will be doing a walking tour, visiting the Kilmainham Gaol, Book of Kells, cathedral's and the castle. On the night of the 5th we are going to the Irish House Party.
6th: Driving to Kinsale. Enroute we will see Rock of Cashel and Blarney Castle. Spending night in Kinsale.
7th. Drive to Beara peninsula for the loop (via a quick visit in Kilmurry Parish) followed by a night in Kenmare.
8th. Early morning to do the Ring of Kerry then drive to Dingle for the night.
9th. Ring of Dingle and explore.
10th: Drive to Cliffs of Moher then to Limerick for the night.
11th: Drive to Shannon airport for the flight home.
I think it looks fine. You will have some long driving days but you also have a two-night stay in Dublin as well as in Dingle. When on the Beara Peninsula look for Josie's Restaurant.
I assume you chose Limerick for your last night because of proximity to Shannon Airport? You may be better off staying in Bunratty instead. That way you won't have to fight rush hour in Limerick. Plus Bunratty has plenty of good places to stay and is 10 minutes from the airport.
We're staying in Limerick so we can visit a town and hotel that share our last name, we thought it would be pretty neat as it's not a very common last name, especially in the United States.