I have taken our dog on several trips....ven tho I prefer to leave her at home. She is a small westie. I believe that United allows one carry-on animal per cabin, $80 per direction. Out dog goes to sleep before take-off, and often only wakes upon touch-down.
I have heard some animals wimper, as they are afraid, and some cats meow. But I have never been on a flight during which the dog barked.
(Our dog has only flown F.)