Welcome aboard, Melanie!
Each Port Adventure lists ages allowed on that particular adventure. If it says 0-2 for an infant price, then you know your little one can join you. Some do not charge for that age, but they are only allowed if that age range is listed. If it shows, for example, 5 and up, you will not have the option to add your baby, as he or she would not be allowed on that particular adventure.
As you look at the Port Adventures, click on the side where it says "Family Adventures". This will narrow the adventures to the ones that even young children can do.
I highly recommend the
Boatswain's Adventure Marine Park in Grand Cayman. My son and I absolutely loved exploring that park, interacting with the sea turtles and viewing the other marine life there. We could have spent the whole day there! Your little one can join you on that adventure.
In Cozumel, either the
Ruins & Beach Tour or the
Beach Break are both great adventures that I've taken. The beach is the same for both, with lots to offer, however only the Beach Break included admission into the kids' waterpark which your little one might really like! I like the Ruins and Beach tour because we were able to enjoy some history and culture at the ruins before heading to relax and play at the beach.
Check out the other Family Adventures, as there are quite a few exciting ones for young families! Have fun as you continue to plan, Melanie!