Greetings from Ireland.
The itinerary is great and perfectly doable.
On a trip like this I'd recommend dropping the overnight in Kenmare (an afternoon or a few hours coffees-stop there is ample) and adding a night in Kinsale to have a nice base for 2 nights.
Or maybe an extra night in Dingle. I say this not because I have a B&B there but because
1. Dingle village and peninsula has so much to see and do, it can justify 3 nights. Its Ricks favourite.
2. I also have a 6 year old daughter!
We are from the North, and split our time between Derry and our new home in Dingle (these last 4 years) when I am not on the road guiding for Rick.
On trips around Ireland with our 6 year old, Dingle is a life-saver because of activities available there such as horse-riding, dolphin trips, the excellent aquarium, the indoor climbing wall etc etc
Galway and Dublin have lots for your daughter to do. I never thought I would ever write the following line of recommendation in a Rick Steves Travel Forum, but you should consider bringing her to the 'National Leprechaun Museum' in the city-centre! :)
Best wishes on the journey. In august the Dingle funfair/carnival will be in full swing, we might run into you there with a posse of boisterous Irish 6 year olds and swop stories!
le meas/with respect
Stephen McPhilemy
Rick Steves Ireland tour-guide
Dingle and Derry