Can you use baby shampoo on your puppy?

No. I used to work in an animal hospital bathing dogs and this is what we were told:

Because baby shampoo is very gentle on the eyes, many people assume that it is also gentle on the skin. Babies spend a lot of time laying on their heads and also often develop cradle cap, and therefore require a harsher shampoo. All human shampoos also have a different pH balance than pet shampoos. Dogs (and cats) have much thinner and less oily skin than humans. You should only use specifically made for pets on your pet. Your local pet supplies store should have a decent selection of these, and your veterinarian may also sell some as well.