How nice that you'll be with us in Dublin for the holidays season!
The Dublin's New Year's festival program can be found on their website
by clicking on the 3 different venues of the festival. I found a family friendly event
at Dublin Castle on the 31st you may be interested in. Some events are free as well. :)
Speaking of things to do in Dublin with your child, we have a previous forum thread
with suggestions for families in Dublin and beyond. I also found the Family Fun website
to be a good place to look.
Let us know how your plans are coming along.