Ireland week between Christmas and New Years

It will also be dark. Look closely at sunrise/sunset times. While I think driving is the best way to see Ireland I would not want to be driving unfamiliar, narrow roads on the left in the dark.

With just a week, maybe you'd be happy just visiting Dublin and perhaps Befast. You wouldn't need a car, there's plenty to see. Daylight hours will be limited, and the weather won't be conducive to long drives. Cold but also very wet.

Went 12/26/18-1/4/19, stayed across the river from the Custom House, which gave us incredibly comfortable (i.e., warm and dry) seats for the NYE fireworks display. Did the Dead Zoo, EPIC, which we mostly had to ourselves--no appointments, just walked in. A lot of holiday stuff was still going on (zoo lights, Xmas market at Malahide Castle). The 1st was DEAD. Just about everything was closed, and there was no one on the streets at all. It was something else! Christmas will be the same. I'm not sure there's any buses or trains that day.
Re: the weather. It's a different kind of cold. We arrived there from Paris, which was colder. Ireland felt colder because of the dampness. I am from PNW, so I am used to both the weather and the very short days. Someone an another post commented about the combination of short days, wet weather and driving being less than ideal. Also, lots of the scenery might be hidden behind fog. I would maybe make it a mostly city trip. Go to Belfast or Galway or Cork as a side trip. All are accessible by train.
Bottom line: yes, it's a good time to go, but no, I don't think it's a good time to do the traditional Ireland road trip/RS suggested itinerary. It's a great time to hunker down in the pubs, eating the Sunday roast and meat pies, visiting the museums, celebrating the holidays.
Have a great time!!!