Conventional guns are not "registered" in free America. (Only a few jurisdictions like NYC, DC, and maybe still Chicago, have laws requiring licensing of gun owners and registration of firearms.)
The interstate transfer of guns between individuals/owners is regulated by federal law and must be conducted by Federal Firearm Licensees (FFLs). Many states also regulate certain intrastate transfer of guns (e.g., handguns, or transfers to individuals who are not immediate family members). For a fee any FFL local to you can ensure that any transfer is compliant with local, state, and federal law.
In general inheritance and transfer between family members is not restricted, so long as the receiver is not a "prohibited person" ineligible to possess firearms. (Though, again, the details of this vary by jurisdiction and change frequently.)
In the situation described, if you are not a prohibited person, you could "inherit" the gun in Florida without any paperwork and simply mail it to yourself in Virginia. If you are uncertain or want to ensure that no laws are broken in that process, have the gun mailed to an FFL local to where you live, and pay the FFL to "transfer" it to you.