I left my airport job in 1974 so my recall will be less than perfect. What you were allowed to do back then was first determined by law and then by airline policy. Maybe small pets were allowed back then but that's not what I recall.
I think all he has to do to fly with the cat is let them know, put him in a cage, and put him under the seat. He's been traveling overseas with the cat for about 10 years..... South America, Europe, Asia......... It's really pretty remarkable.
The cat is big, but will sit in a small cage for very long flights and not make a sound.
I agree that if the bunny was in cargo, that could well have killed him.