I think your plan...given your experience is rather foolish. It is no cakewalk to the Caribe and planning to do so with a baby means you will have to singlehand and keep watch and take care of baby with two inexperienced sailors in a boat that is capable but not WELL suited for the trip. This is not to dump on your dream but to suggest it needs major modification:
1. Get the boat and wander around the Bahamas...700 islands...lots of EASY sailing and wonderful spots. Head north and explore the ICW & chesapeake when hurricane season approaches,... or head south to the DR and wait it out there if you want a rustic/3rd world experience (though I wouldn't take a baby there).
2. Buy the boat in the Caribe and eliminate the hard part. Learn to sail in the Virgin Islands where it is pretty safe and protected. It is easier sailing BACK to florida with the tradewinds at your back and some experience under your belt.
No longer posting. Reach me by PM!