I'd call the airline that you are flying on and talk to them. Some airlines have different requirements. When I went to Texas, I shipped the gun to myself because after leaving the ranch I was spending a few days in a different city, taking a flight there and staying in a hotel. It turns out that shipping the gun cost about the same $$ as paying the baggage fees.
My only advice is use a good case, and make sure that you verify the gun stilll shoots to the same POI once you reach your final destination. Have a fun trip!
