unless things have changed, your drivers license was also your pistol permit in fla.
http://www.nraila.org/statelawpdfs/FLSL.pdf
If I understand the NRA summary of Florida’s gun regulations, a properly identified, qualified adult can buy a long gun with just an instant check. But there is a three day waiting period for a handgun and, will certain travel exceptions, you need a concealed carry permit to have a handgun on you outside your dwelling place.