Because the laws on registration and insurance vary widely from state to state, it's a good idea to check the DMV website for whatever state you are buying a bike from and see what their requirements are in order to buy the bike and leave the state with it. For example, some states allow you to just sign the back of a title in order to transfer ownership, some require that you go to a notary tag service to transfer the title (like PA does), some states need the signatures notarized, etc.
If you can't get the info you need from the FL DMV site, call any Florida Highway Patrol station and ask them what you need to do.
It's probably best to call your current insurance carrier, explain to him what you're planning to do, and ask him what you need to do to be covered. He's the expert.
"No matter where you go, there you are."