What you really need to bring is your ATM card to get euros at a great exchange rate once you arrive in Ireland. For the best info about using your cash card in Europe, read Rick Steves' article at http://www.ricksteves.com/plan/tips/cash-machine-atm-tips.htm
I also would bring about $200 in USA $20s for emergency. I usually bring it all the dollars back with me home. almost 5 years ago
You can certainly bring USD $ but will then have to exchange them for either Euros if you are going to the Republic of Ireland, or British Pounds if you are going to Northern Ireland.
ATMs are available so you may wish to use those as well? almost 5 years ago