I just found the number for the Florida Dept of Law Enforcement Firearms division, and gave them a call.
They said that out-of-state residents cannot purchase handguns in Florida. However, out-of-state residents may purchase long-guns.
I told him I have a Virginia CCW permit, and he said it doesn't matter. I would need to be a Florida resident to buy a handgun.
Well, that answers my question. Guess I'm not going to bother going to the gun show.