Babyzilla is two and a half now and too big for me to carry very long anymore, but I used to carry him all the time in slings and wraps. Which you are also not allowed to use on a plane. Because that extra layer of fabric holding your baby to you in addition to your arms in the event of a crash is not a FAA approved device. Despite how much sense it makes to add an extra layer of protection to keep the baby with you AND it can free up your arms in the event of a crash and emergency landing. But no mom and pop sling maker is going to tackle the FAA. But they can be used after take off at least.
The best travel tip I got was to take a small blanket and tuck one side under the baby's seat and the other into the front seat pocket to make a little catch basin for dropped toys. It doesn't work well for lap children, but if you've ever had to root around for a dropped toy while you baby is screaming, there's drinks on your tray and the seat in front of you is reclined, you'll thank the heavens for a way to keep that from happening more than once!