As others have said, don't call the language Gaelic, call it Irish. If you must say Gaelic then note that the Irish and Scots pronounce it differently.
If you want to specifically refer to the bit of the island which is not Northern Ireland then say The Republic (of Ireland) rather than Southern (Ireland). Better still, don't.
Learning Irish is hard, way harder than French, Spanish, or German. For a start the spelling is very complex.
If you are unlucky you may encounter the occasional Irish only sign. I got stuck in a small road once because the sign which said: "Road suitable only for horses", was in Irish only. However, you will be a remarkable linguist if you learn Irish well enough to understand that during a short holiday.
As Todd says, you will hear a few Irish words, e.g.Taoiseach, though I think tea shock is a closer approximation. Gardaí is police and you will commonly hear them called "The Guards".
Relax, have a Guinness or three and a couple of whiskeys (note the spelling) and concentrate on having some fun.
During a recent trip, the languages that I heard, in order of frequency, were: English, Tagalog (Filipino), Polish, and Irish. Apart from the TV, the only Irish was my mum talking to the band in the pub after a couple of glasses of Jameson.