Introducing the baby to the dog
The introduction should be controlled and calm. A few suggestions are as follows:
When mother and child come home from the hospital, it is best if mother greets the dog without the baby present.  The baby should be held by another family member or, better still, put in another room while the mother and dog greet each other. This way, you can avoid reprimanding an excited dog that merely wants to greet the owner and that may jump at the baby in an attempt to get near the mother.

Owners should allow some time for the dog to get used to the smells and sounds of the baby, which to it are the presence of another creature in the house. Later, when the level of excitement in the household has decreased and the dog appears relaxed, the baby and dog can be introduced to each other.

One parent should attend to the baby and the other to the dog. The dog should be in a sit/stay or down/stay and on a leash. If there is any concern that the dog may leap at the baby, a halter or muzzle should be placed on the dog. (The dog should already be used to the muzzle prior to this introduction.) The dog should be allowed to see the baby from 10 to 15 feet away. Then either the dog or baby should be brought closer to the other, slowly, one foot at a time. If the dog remains calm and under control, it might be allowed to sniff the baby, again from a safe distance. If the dog is extremely excited, however, this progression should not be attempted. If the dog has a history of predatory or aggressive behaviors, it may take many introductions before dog and baby are close enough for the dog to investigate the baby closely.

Err on the side of caution when determining when your dog is ready to approach your baby close enough to actually sniff the baby. Over a period of days, however, your dog should be allowed to smell the baby up close. After several introductions, and when it is clear that the dog is not going to nip or lunge at the baby, you can allow your dog off the leash near your infant. (This does not mean unsupervised visitation or that you should lay the child down for the dog to investigate it.) As a further precaution, the dog can continue to wear a comfortable muzzle when around the baby.
Children and babies should never be left unsupervised with the dog. They do not speak the same language and that often results in misunderstanding