We moved here with our 3 & 1 year old, so I have a few pieces of advice that you can consider.
1. Don't bring the car seat (you'll probably not use it). They are big and bulky and not necessary on this island.
2. If your baby likes to play with beach toys, bring a few small ones. My babies have a few, but play with shells and sticks mostly. There are stores in town that sell beach toys very inexpensively also.
3. Sun hat! Definitely a sun hat.
The less stuff you bring the better. I see tourist bring 2 suitcases just for the babies needs and have to laugh. Babies really don't need that much stuff.
If this is your first baby, you will most certainly obscenely overpack