Another alternative is to mail/ship it (insured of course) to yourself, care of your folks at their Florida address.  This is perfectly legal (I think you can look it up on the ATF web page), and does not require any particular paperwork or involvement of anyone else.  

People sometimes do this when going hunting, to avoid the hassle of having to drag the case to the airport (and occasionally having to deal with airline employees who are not sure about the rules).