Generally speaking, it’s all right to allow your pet near your new baby, as long as the pet is well behaved and you are there to supervise.
It’s common for a pet, who has until recently been the focus of the family’s attention, to become jealous of a new baby. You should allow your pet to become accustomed to this new member of your household while in your presence. Continue to give your pet plenty of attention, both when your baby is present and when you have time alone with your pet. This will keep the jealous behavior to a minimum.
If your pet shows any aggressive or hostile behavior toward your infant, you should quickly reprimand him. He’ll learn fast what behavior is allowed near the baby. If your pet doesn’t respond well to your reprimands, though, get help from a professional trainer.
When your baby is very young, I’d recommend not allowing the family dog or cat to lick your baby’s face. This could transmit infectious material (such as feces) into the baby’s mouth or eyes. As your baby grows older, her immune system will get much stronger and she can play with and even be licked by your pet without any consequences.