Celtic/Christian Ideas? - Very little time in early January in Ireland.

An internet search shows me that, on the official webpage, The Irish National Stud and Gardens are open to the public from 1 February to 28 November inclusive. That's 2014, I would be surprised if 2015 were different in a big way, so that may be difficult for you.

Rent the car. More freedom and as you have only a couple of days the best option for travel. Daylight hours will be short so you'll need to plan accordingly. The monastic settlement at Glendalough is a must see in my opinion. Beautiful, historic, Christian. I'd also add the Rock of Cashel. Book Kells is great as is the attached library.

Locals may have secret favorites, but Rick Steves does not; he publishes all in his Ireland guidebook.

Glendalough, south of Dublin, is an ancient monastic settlement ruin which is a very good day trip from Dublin (or en route to somewhere else). They have a fascinating little museum there, and if the weather cooperates you could walk down to the lake, too.

B&Bs should be easy to find (though some will be closed for the winter), and generally the hosts are a wealth of information about the local area, and will want to tell you all about what to see and do. I would definitely vote for renting a car, particularly since you want to get to some smaller areas in a short time.

St Brigid's well is outside of Liscannor, on the road to the Cliffs of Moher. The Cliffs would be an easy addition to your plans and they are open 364 days a year. Of course, you know your child better than I do, but I can't imagine an 8 yr old getting much out of seeing the Book of Kells. Understanding the conditions under which it was created, and preserved throughout the centuries, isn't something that a child can generally appreciate. You shouldn't have any problem with having to wait in line in January, though you might want to check whether or not they will be open that early in the year.

You know your daughter better than anyone. I just came back from Ireland and seeing the Book of Kells was a highlight of my trip. The admission is 10 euros for adults, not sure about children. You can buy an excellent audioguide for 5 euros, which you keep. The exhibit that you go through before seeing the actual book is very well done, very informative with large blow-ups of pages from the book, and the blow-ups are excellent for seeing and appreciating the details in calligraphy/embellishment. If your daughter likes visiting museums, she might find this worthwhile. It is a real privilege to see the Book of Kells.
Whatever you do, dress warmly.

Book of Kells is free for children under 12. Closed New Year's Day. Open Monday - Saturday 09:30 - 17:00, Sunday (October - April) 12:00 - 16:30.

site of our lady of Knock?
if you go to the National Stud....within it is st fichara's garden, there are some reproduced monastic cells..... and within those are some amazing Waterford ferns and orchids......an exquisite place, nice little cafeteria and gift shop as well.

is it Hill of Tara where st Patrick first lit the Paschal fire ?
I think it was Brigit's well where I was amazed at the things left behind by the faithful....
perhps also a ring fort?