I would suggest that at three, your daughter is too young to appreciate the pitfalls of a 'new member' of the family. Children of that age are too young to appreciate that animals feel pain when poked or pinched, or teased, all natrual behaviour for a little one, but it can provoke retaliation in even the most passive pet. Similarly, a pet may resent what it sees as a fellow 'pack member' usurping the pet's place in the pecking order, which can lead to problems. If you are determined to buy a pet, why not try a fish or bird, something which won't require petting, but can start your child on the road to learning responsible pet keeping.