We have a daughter that is 3 and a half (4 in July) and a son that is 2 (TURNED 2 TODAY....CAN'T BELIEVE IT!) Anyway, they are both good with our dogs. They have had to learn what gentle is. In fact, my youngest will pet our Maltese/Bichon mix puppie and will actually say "gentle" as he is petting Bailey.
We had Harley (our Yorkie) before our children and so they are used to him and vice versa. We also have cats and have had them since they were 10 weeks old. Our children have always been great with them, too! I think that it depends on the child and how they are raised to treat animals. We tell our children that animals do not understand and that we HAVE to be gentle with them because they do not have words like we do so their way of talking to us if we hurt them could be to bite.
I really think each situation is different, just like every child is different.
Tammy