You can pay someone's airfare, and they can take her on the plane with them Although, one of our house cats LOVED the car and rode in the moving truck (with the driver) cross country. For weeks after the trip he'd jump in the car to go for a ride
I've shipped my cat as cargo on regular airlines (usually Northwest) multiple times without issue. She's always unaccompanied -- either I drop her off and family picks her up at the destination, or they drop her off and I pick her up on arrival. I think the cost has been somewhere around $300, and we've done some long flights (Alaska to Ohio and back, Alaska to Texas).
You have to watch the routes -- they won't ship pets if temperatures are predicted to be above or below a certain point. The vet certificate has to be done within a fairly tight timeframe (days?).
I've never had a problem doing this. She's always come through just fine (mad as anything at ME, but she's fine).
Not horse-related, so we're going to close this one, but hopefully the comments thus far were helpful. Also, you could check in on our rideshare thread stickied in Off Course--perhaps your cat could thumb a ride on a trailer going her way...