We started bringing our son at 4 months old. (Land).
In addition to the great suggestions, I'll expand on thing our now 9yo loved over the years -
Michael beans show. Rocked his world. If you are there during high season, make reservations and tell them you have a little one and ask for a table close to the stage.
In addition to the tarpon feeding, our son liked the "tank talk" afterwards on Saba.
Jumping off the rocks at Spring Bay. (Personally, I think it beats the Baths many times over)
The Copper Mine on VG. We went twice when he was nearly 4 yo and we pulled him away in tears each time because he didn't want to leave.
If your child likes pirates, pack swords, eye patches, loot bags, telescopes,etc. $20 worth of gear provided hours of daily entertainment. I swam to shore at Sandy Cay with a bag of costumes and we all dressed up and had a pirate adventure on the island when our son was 5yo.
On STJ, the ruins were a big hit. Also, snorkeling with the turtles at Maho.
Have fun. Our son is starting to cross over into the older years and I wish we would have done twice the trips when he was younger and always delighted with the world.