Um, well, I don't expect someone to be carrying a single shot .22 for defense against an animal. Having more than one round makes a big difference in this case. That having been said, I've had to put down a couple cats and even a Fox with a .22, I always used more than one shot. Yes, a round in the head is likely going to stop an animal, but you WILL have to be able to make a follow up shot, or more if you miss. If you HAVE to kill the animal, don't let it suffer. Animals move fast, at short range you may be better off with a contact weapon.
"Today is victory over yourself of yesterday; tomorrow is your victory over lesser men." - Miyamoto Musashi
[Insert random irrelevant religious quote here]