Whatever you do, do not bring a newborn baby back to a house that has a small puppy in it. Chances are the dog will try to smother the next child, thinking he or she is also a puppy, because it doesn't know better. It will think your little child, roughly smaller than it, is one in the same which leads to a dangerous situation for the little one. Cases have been documented of dogs jumping into cribs, into strollers and otherwise harassing babies. They don't understand that the little one is a child, not a dog, and this limited view makes them view the baby as a playmate. We've all seen dogs play with one another, and it's certainly not a way to handle a baby.
If you have a new puppy and a new baby, there are steps you can take to protect your child. First and foremost is making sure there's no way the puppy will ever get into the nursery. You can do this by creating a half-door to the nursery, not a puppy gate (which many dogs eventually learn how to get over or barrel through). A half-door is basically a door cut in half or three-quarters where you can walk by and see into the nursery without entering. Most parents like to leave the nursery door open, which would allow the puppy entrance, which is not what you want to do in this case. Using a half-door method will give the chance to walk-by and check on your child while maintaining a safe environment for them to grow up in.
Never leave the child alone and take care to make sure the dog can't harm the baby when he or she is in other areas of the house. If this means locking the dog in the backyard or in another room, risk hurting the dog's feelings and relationships with you, because the price of the alternative is just too high to pay. That price is that of the baby's life, and that's not a price any parent ever wants or deserves to pay. Take steps to prevent an accident from happening and protect your baby from the dangers of a new puppy who doesn't know better, just like your child doesn't know better.