I also had a quiet few minutes and decided to plan this out. Assuming EVERYTHING goes well (the drive time listed on Google Maps is the actual time, you never get lost, you never have to stop for a sheep crossing, etc.), here's what I came up with:
DAY ONE - ARRIVE DUBLIN
You don't say what time you arrive, but I know a lot of flights from the east coast land in the morning - sometimes VERY early in the morning. I think the direct flight from Hartford gets in at 4:50am. The worst case of jet lag I ever had was my one-day layover in Dublin. I mainly remember flashes of Trinity College and a tourist shop, and then passing out on the train while my friend tried to keep me awake. But let's assume you land and have no jet lag and see what you want to see (which you don't mention, so maybe one day in Dublin is doable for you).
You leave Dublin at 8am, which means getting up an hour (?) earlier to pack, shower if you wish, and eat breakfast. It's then 1h37m to the Rock of Cashel, putting you there at 9:37am. Say you spend an hour there, leave at 10:37am, arrive Cobh at 11:45am (1h8m drive). Stay for three hours, one of which will likely be taken up by lunch. Leave at 2:45pm, arrive Tralee 4:50pm (1h55m drive). Check in to your hotel, unpack what you need, go to dinner.
Again leave at 8am. I wasn't sure what you meant by "drive the Dingle Peninsula," so I put in three locations that made the loop. Tralee - Dingle (50m); Dingle - Dunquin (35m); Dunquin - Cloghane (50m). If you make no stops, you'll be in Cloghane at 10:15am. From there it's a 2h42m drive to the Cliff of Moher, assuming you catch the ferry RIGHT on time. That puts you into the Cliffs at 12:57, but let's say you also stopped for lunch. Call it 2pm arrival at the cliffs. Stay an hour, drive 11minutes to Doolin, getting you there at 3:11pm for checking in/unpacking/dinner.
Cliffs of Moher to Bru na Boinne is 3h18m. Leave at 8am, arrive 11:18am. Stay two hours, leave 1:18, drive 45minutes to Dublin, putting you in the city at 2:03pm. You don't mention when your flight home is, but I'm assuming it's the next day.
So, yes, your itinerary is doable. You physically can do it. But I would really suggest thinking hard about if you WANT to. This is assuming everything goes exactly plan - and when does that ever happen? It also has you rushing through sites, like the Rock of Cashel, and doesn't include stops, such as ones you'll surely want to take on the Dingle Peninula. Others who have been to and driven in Ireland consistently say that you need to add 25-50% to the drive time given. As AlliM pointed out, your second day has you driving almost 7 hours. It's ultimately your vacation and your choice, but I fear your memories of this trip will be of looking out the car window.