I ship quite often. I use a small dog plastic kennel with a perch added near the bottom of it. I shred up some newspaper and put on the bottom, then I put on the bottom some nuts, pellets, fresh fruit, and on the door I add a bowl for water.
Delta and Continental have a special program for shipping pets, and they look after them pretty good.
Just yesterday I shipped an Eclectus to Los Angeles, CA and a caique to Burl, VT. We did have a problem with the VT flight being late, but other than that all was good.
The birds usually get along just fine while in flight. I imagine they are forging around on the bottom of their kennels.