My only advice is don't expect your dog to know how to act and behave around a newborn, or kids in general. I completely agree with EAO76 that she could be reacting to your nervousness. You have to be the one to teach her her boundaries and teach her what is and isn't acceptable behavior around the baby. She has no way of knowing unless she's taught, in a positive way, of course. If your not sure how to teach her in a positive way, definitely enlist the help of a trainer or behaviorist.
It took my dogs a long time to learn how to act around a baby. My daughter is 2 now, and though I trust my dog, I still wouldn't leave my child and my dog alone in a room together unsupervised.
Also, keep in mind that the baby is only a month old, and that your dog has only had a month to adjust to all of the changes that having a newborn brings to a household. It can take a long time for a sensitive dog to adjust to a major change like a new baby in the family.
Good luck, and congrats on your baby!
Amy, Mom to:
Rambo- Fawn, Male, born 5/9/2005
RIP Vegas- Yellow Lab 2/5/04-3/23/10