Personnaly, when we are going to Cork from Carlow, we go cross country to Abbeyleix via Spink and the Swan and then on from there, you'll have a motorway all the way from just outside Durrow to the Jack Lynch tunnel (toll bridge in Watergrasshill). Only issue is that given the weather, the Carlow Abbeyleix road may be seriously dodgy so may be best to head for Port Laoise. Personally I think you'll make better headway that way.
Alternative would be down to Waterford, Waterford bypass is open (toll bridge) but again, crap roads in Kilkenny and a lot of flooding down there.
Either way you can't win, at the minute, until the M9 is finished it's impossible to get out of Carlow without going on some bad road