FAA rules for shipping firearms are VERY strict, and your luggage is actually handled with MUCH greater care and security if it has a declared firearm in it. If a declared firearm goes missing or the luggage is damaged, then EVERYONE in the luggage-handling chain gets dragged through the mill to figure out what happened. So they tend to handle them with kid gloves.
This is actualy a well-kept secret with high-tech business travelers. Get a big "road box" like rock bands use for their amplifiers, and put all your delicate, expensive computers, projectors, etc. in that case. Then get an inexpensive handgun and put THAT in the case too, and declare it with the airline. They will usually take you out of the regular baggage-check line and rush you through to the TSA people, who will then check it out. You MUST use non-TSA locks--REAL locks that ONLY you can open--to secure the case. You open it, show them the firearm, they declare it on their paperwork, put a copy in the case, and then you lock it back up, and it goes to baggage claim. You get it at the other en of your flight, with nary a scratch on the case.
Or that's how it works in theory...
But dude, Jacksonvile's only about 7 hours drive to DC. Why not just drive? It would be MUCH easier if you are planning to have a firearm in VA while you're up there. If youhave a NC CHP, it's good-to-go in VA too. Driving would be a LOT cheaper than flying, if you haven't bought your tickets yet.
But if you DO fly, mae sure to book your flight into Dulles or Reagan which are in VA. You do NOT want to arrive in BWI, which is near Baltimore. Getting your gu at the airpoort would be easy enough, but then you'd have to worry about transporting it in and through MD, and that would NOT be a fun way to spend your weekend...
Here is an article that tells it more clearly than I do: