If you want your firearm with you in Florida and it will be legal to have it there, ship it to yourself in care of your destination, ans instruct whoever receives the package to not open it.
There are numerous instances of folks with NY or NJ layovers trying to declare a firearm being arrested for volating the state's laws requiring a license from them to even posses a firearm in that state. There are many court rulings that go both ways - upholding the arrest and conviction seems IIRC to outnumber not guilty findings. A quick Google search ought to give you enough of a case of the willies to ship ahead instead of fly with.
PS (edited to add) Be sure you will be covered carrying concealed in Florida. There is no OC there and threy only recognize certain other states' permits.