Check out these pages of the Cruising Wiki: YACHT CREWING INFORMATION
HITCHHIKING THE OCEANS AS SAILING CREW
Key West might be a great place for your vacation, but it's not a great place to find cruisers leaving for someplace else. January and February are not good months for anybody leaving the US. Boats going to the Bahamas usually leave from Florida - Miami, Lake Worth - in November, sometimes waiting a couple weeks for a reasonable weather window.
You could find crewed charters in the Keys, the Bahamas (interesting one on Andros Island) around that time.
Passages to the Caribbean from Florida can be very slow, taking months if the cruiser chooses Van Sant's "thornless path", or just weeks if they tough it out and head straight for Puerto Rico or the Virgin Islands. Hard work getting there, though once in the Caribbean it's all worth the effort. But not if you arrived after a hard 3-week bashing only to find a flight back to the US without having a chance to enjoy the destination.