NO NO NO. Do not bite your puppy or smack it on the nose.
This will only make it bite more either through pain or fear.You don't say how old you puppy or little girl is, but I would not let a puppy play with a baby or toddler until both of them know how to behave with each other. If the puppy bites you, then make a yelping noise like another puppy would, and quickly withdraw your hand and ignore the puppy. This is how they learn when playing with each other or with their mum. Make sure the puppy has plenty of toys/chews to play with and chew on, as puppies need to chew to loosen their baby teeth and help the adult ones come through. Distract the puppy if it is playing rough and give it something to play with or chew on. Have a puppy play pen or cage so it has somewhere it can get away to sleep and rest away from the baby.