I know for a fact that you can carry on small animals as long as they are in an appropriate "cage", as you will. The carry-on has to fit under the seat in front of you... I don't see how a turtle could be more trouble than a yippy little dog! Have you tried American Airlines, TWA, Spirit Airlines, etc.?
If you decide to ship your turt, you have to overnight her via Fedex. You need to pack her in a plastic container w/airholes in some damp moss to cushion her from being thrown around too much. Then also cushion the plastic container w/paper towels or something like it. Make sure it says "fragile", "live animal"' and "this side up"!!!
UPS does not allow the shipment of live animals even though they have (unknowingly!) delivered live turtles to people.
Good Luck!
