It occurs to me that birds aren't the only sources of verbs; you can dog someone (or hound them), fawn over them, snake around obstacles or weasel out of them, pig out (and hog all the food), horse around, badger someone, ape them or fox them, leech from them, ram them, wolf something down, rabbit on, or apparently if you're American, skunk someone - presumably at Beetle.

You can also act the goat, be sheepish or make sheep's eyes, be catty or mousy (or crabby), be bullish or a cow, smell something fishy, and whale on someone, although heavens knows where that one came from.

Parrot is a bird verb we've not yet had.