The problem for you is..according to handgunlaw.us http://www.handgunlaw.us/states/florida.pdf
Florida does not honor what they deem "Non-Resident" permits. Meaning, once you establish official residency in Florida, you are no longer a resident of Virginia, making your permit a "Non-Resident" one. Florida honors your permit, along with many, however, they require you to be a resident of the state of issue. Meaning, that once you become a FL resident, your Virginia permit is no good here anymore.
I suggest, if you have the time before you move, that you apply for a Florida CWFL (concealed weapons and firearms license) now. It's fairly easy. Just go to this website,
and follow the links to request an application. A copy of your Virginia permit, I believe, will suffice for proof of training and you'll just have to have your local PD or Sheriff office do your finger prints, then, all you do is stuff everything in the envelope provided, along with your check, and send it in (HIGHLY recommend registered return receipt mail). You should have your license in a couple months or so, and could be as early as a few weeks. Reported time lines seem to be varying right now.
If you don't have the time, call the DOACS' nearest regional office to where you'll be moving NOW and schedule an appointment date after you get here. They handle everything. All you need to take with you is your proof of training and your checkbook. You'll have your license within a few weeks.
You should be able to find a regional office near where you're moving here....
Good luck and safe travels.