Sorry, I think your daughter is too young to "have" a puppy. Wait until she is older and understands how to behave with animals - especially if she is fearful now.

My suggestion, try to make an acquaintance with a family who already has a dog. Then she can learn how a family pet has to be treated properly - plus, you don't have to spend any money or take it to be spayed/neutered/vaccinated.

Once she learns how to behave around animals (little kids are "grabbers" especially at 2 year of age) both she and your new pet will be much happier. Remember, dogs can't talk, they can only express their feelings through body language, barking, running and hiding, and - as a last resort to protect themselves, biting.

Teach your child first, then get a pet. You'll all be much happier.