It’s not a naive question at all. Yes, flying in the USA is different, but it’s not going to cause you any problems. Any flight instructor who does his job properly will make sure you are well versed in local procedures before he signs you off – you can make it easier by reading up before you go. Flyer do a useful little book on flying in Florida, and there’s various other guides you can buy.
Flying out there is very straightforward. I’ve no experience of Irish airspace, but the radio is certainly more laid back than in the UK. ATC are very helpful; the flight following service is excellent, there are no landing fees and they are quite happy to let you into busy airports (I’ve done a parallel approach into Palm Beach next to an A320 – can you imagine that in the UK?).
If you’re still not comfortable after a few hours, you could always get an instructor to come up with you as safety pilot – you’ll probably end up doing much more challenging flying than you would on your own, and I’d bet it would still be cheaper than flying at home.