My son is now 5 and we have been traveling to the islands with him since he was 6 months. We actual took him to St. Martin when he was about 9 months. My recomendation would be to make sure to bring plenty of diapers since it can be very expensive to buy them on the islands.
We also brought a pop up kid tent so he would have a nice shaded place to nap while we were at the beach. If you prefer the pool, make sure the tent has a thick bottom or bring extra towels to pad since the concret can get hot.