I usually cape it, freeze it, put it in a small cooler and take it through with me as a checked bag or even a carry on
I'm a little paranoid because several years ago I harvested a beautiful double bearded Merriam in Wyoming that I decided to have mounted, so I caped it out, froze it up and shipped it "Next Day" through UPS. Unfortunately for me they lost it and a week later when they finally found it...well let's just say it wasn't pretty. Lol.