B.B.
Have a great time, we love that area! We have the Graco travel set (stroller and car seat) and brought both on our trips, you can keep your son in the stroller through security all the way to the gate. If you choose to buy a separate seat for him, you can strap most car seats into the seat (you may want to check the airline to make sure yours will work), if you do not purchase a seat, the folks at the airline will check in the car seat and stroller just before you enter the plane and have them waiting for you when you exit the plane at landing. I travelled with my son when he was about 4 months the first time and I tried to purhase a plane ticket close to when he naturally napped. I also have an ultimate baby wrap that he used to love to sleep in. 30 min or so before the flight, I changed him, put him in the wrap, walked around and lulled him to sleep. I had a pacifier and bottle on hand for landing and take off- it helps them with ear pressure. Most young babies sleep on the plane as the 'white noise' sound of the engine lulls them.
I would assume the resort would have a crib, but you may want to check with them beforehand. I am not sure how the taxi's or shuttles work, but if you bring the carseat with you, it may make things easier. If you plan to have him in the sun at all, I would look at some sunscreens and test some on his skin before you go to make sure he is not allergic to it. A big bucket hat that has a velcro strap under his chin would be great to pack also.
Other than that, have a great time! It sounds like a lot of fun!