That itinerary, with that many days, will be tight.
It takes longer to get around Ireland than most first-time visitors expect. And it's a long way to the southwest, where many of the most interesting things are. I would look to prioritize and cut some things. There are a couple tricks you can use to shave a day here or there, such as:
1 - Save Dublin for the end of your trip (you have to spend the night there anyway before you fly out).
2 - Upon landing in Ireland, take the bus straight from the airport to Galway. You'll be a wreck from exhaustion and jetlag that first arrival day anyway, you have no business getting behind the wheel and driving in the shape you'll be in; the bus from the airport is super easy, drops you right in Galway.
3 - Get a good night's sleep, pick up your car the next morning in Galway, and off you go.
Figure out the rest of your plans in the west/southwest (you will need to be ruthless and prioritize).
4 - When you are done with your car, you don't need to drive it all the way back to Dublin. Drop it someplace where you can find a rental agency that's near a rail station, take the train back to Dublin.
With your list of places you want to go, with the distances/time required between places, and the time you have, you will need to trim things to make it work. You will need to trade off days in Dublin for some time elsewhere (and maybe still cut some stops from your list).
Hope that helps.