I took Sam to Nevis when he was almost 3 February 2007.
I just got back from St Lucia with Sam and Josie. Literally got back on Friday.
Our flight time is around 8 hours from here.
It was honestly honestly easy both times. Naps were not remotely a problem as the plane is like the world's best white noise machine with the hum of the engine. I just bfed Josie to sleep. There were kids movies on the entertainment system. I took lots of books. With snacks, books, chats, some drawing, a little walk around, naps - the time flew. When we arrived I kept them up as long as I could (we have a 4 hour time difference) and they did really well.
As for when you are there. I used more nappies than I was expecting as I forgot to factor in changing in and out of swimming costumes and getting wet and sandy. I used factor 50 sunblock at all times, sunhats and all-in-one 'Aussie cossies'. We had a couple of rainy afternoons and light raincoats were useful.
In the Caribbean hotels are very kid friendly, meals are easy, staff are incredibly friendly. Airports are not super duper so the flight home and waiting around in an airport with limited facilities was not brilliant. Where are you going?