My DD did... and we didn't allow it. (she is turning 1 year next week. O_O)If she hits us, pulls hair, bites, or anything like that we would first correct her by stopping the action and telling her "we don't ____". If she tried it again, she would get put down, told again "We don't _____." and ignored (we would keep an eye on her, but not give her any attention) for a minute or two. Long enough to know that we weren't going to play with her if she was going to do that. They don't see it as fighting or being mean, but they can be taught what is and is not acceptable behavior. She still tries to push her limits of course, but she has learned that if we tell her "we don't ______" after she tries something, she won't try it again. (usually. lol)
It worked with our animals too. She used to run up to the dogs and grab handfuls of fur, and yank. Or just start pounding away on them. (poor, patient dogs. lol) We would always immediately stop her and help her pet them nicely and say 'Nice hands! We have to use our nice hands to pet the doggie.' If she tried hitting them again, she was taken away from them and not allowed to play with them again for a couple minutes. Now she walks up to them and pats them nicely.