Actually, licking the baby's hand is a sign of affection. My dogs lick to show affection - so I don't know if I would be worried too much. Of course, caution is the better part of valor so I wouldn't leave the baby unattended in the same room as the dog. But, remember that the dog has been the "baby" for the past years so she will feel a little left out if all her humans are going gaga over the baby and not her. Human babies are strange creatures to dogs - weird noises and smells, oh my! - so their natural curiosity is aroused. Just be patient with your dog, let her have a chance to get to know the baby - just like we teach our children to be gentle with our pets we have to teach our older pets to be gentle with our children.
When I brought my son him from the hospital 14 years ago I had cats. One which was particularly attached to me and I was concerned that he would be jealous of baby. Well, since the baby was always in my arms, nursing and what not, the cat just laid down on the other side of me - he sniffed and smelled the baby then started to groom the baby. At that point I stopped him - cat spit on babies, not so much - But it did alleviate my worries - that cat became my child's best friend.
Just be patient and reassure you dog that she is still an important part of the family. Dogs and kids are great together and I bet they wind up being best friends.