we flew to the USA when mu DD was 7 m.o. We noticed some people had paid for an extra seat for their babies/toddlers and brought their car seats along and strapped the car seat to the airline seat and voila! Though your baby is probably not ready for the turned-around car seat yet.

Did you know that they also have sky-cots? They're just little capsule type things they secure to the bulkhead, and if you're lucky, baby will sleep at least part of the way there.

Otherwise they do have seatbelts that attach to your seatbelt.

Hope that helps