The other alternative is to purchase a lot that already has an active permit, allowing you to begin building right away. Bear in mind that you will need to stay within the confines of what the existing permit is for.
There is a wide variety of preoprties Keys-wide that currently are for sale and have active permits. Follow the link below to view the list.
If you would like a complete guide to understanding the residential building building permit process, click here for an article that will provide a great deal of information