Lisa, I can't speak to the NI part of your trip. But I can talk to Donegal, Clare & Dingle.
We just spent 3 nights in Donegal this past November. We stayed at The Arches B&B about 6KM north of Donegal town on Lough Eske. It is an awesome place, hostess and gorgeous view of the Blue Stack Mountains. We took a day trip up north thru Letterkenny to Glenveagh National Park. Gorgeous scenery and castle. Another day trip we did was over to the Slieve League Cliffs. I think they are more remote and rugged than the Cliffs of Moher. If you go to Youtube, there are several good videos of Slieve League.
From Donegal, it's a pretty good drive 3 - 4 hours south to County Clare. We stayed at a farmhouse B&B between Doolin and the Cliffs of Moher. We arrived at the Cliffs at sunset - the views were breathtaking.
From the Cliffs of Moher, it's a 4 to 5 hour drive to Dingle. There is a ferry you can take to avoid driving thru Limerick that will save serious time.
We stayed at The Lighthouse B&B in Dingle and loved it! You might cut back to 4 nights and go to Cashel your last night. If you're flying out of Shannon, it's an easy drive from Cashel to Shannon. Maybe an hour and half. The Rock of Cashel is a definite must do and the Abbey very close to it. It's cute quaint little town.
While you're in Dingle be sure to do the Slea Head drive. Well documented in RS' guidebook. With all the stops, it's about 4 hours of gorgeous scenery. You can also venture over to Killarney and tour the Muckross House and then it's a short drive to Killarney National Park and the Torc Waterfalls.
One last note. You didn't say if you've ever driven in Ireland. The road signage is nothing like we have here in the states AND I usually got lost everyday. But I finally decided I was getting to see something I hadn't planned on.
The people are the best! We are already planning a return trip to just be Donegal and Dingle.
Safe and happy travels!