We are flying with a 22month old, but not buying him a ticket. He is able to ride on our lap. If we wanted to bring his car seat we would have had to buy him a ticket.
I found this
http://www.babybair.com/ Baby Bair, it secures your child to your lap belt to protect your child against the unexpected dangers of turbulence and to keep your child safely on your lap during flight.
It is NOT approved for use in a car.
Sounds neat. You can find it used for less money on ebay.
-nat