I’m gonna back up bashere, here. If you dog is giving the classic “play bow”, she probably sees the baby as a pup and playmate. (A Lab cross… probably a “play bow”.) There are also some other body language clues, licking the baby’s ears, rolling on her back, “yippy” barks and growls (even growls- theatrical non-threatening growls- can be good with dogs), stiff legged hopping.
Now I’m gonna back up Holly. Tail-wagging can be either happiness or aggression. Long, sweeping wags = happy. Short, slow twitches = stress, which can easily turn to aggression. And like bashere said, even play nips and bumps can turn bad, fast.
Is the baby a baby baby, or sitting up and moving around? If the baby is moving around, your dog could get a sock in the eye.
Both my boys were around dogs from the first day. (Two dogs were ours, and the neighbors’ dogs, and other family dogs.) Nothing bad has happened yet. Of course the boys don’t get to play with my sister’s older dog, she’s kinda crabby. And they never get to play with dogs we don’t know. And there’s always an adult around to “referee”. There’s alot of rough play with my older son, but when either he or the dog has had enough, they get split up. The one-year-old hugs, and pats, and smacks, and pulls on the dogs. He gets to play with the dogs who like him anyway (untill the dog has had enough), and the rest just avoid him. So dogs and babies can be well matched.
You might consider taking you dog to Obedience Training. It’s never too late. And being around other dogs and strange people might help her in new situations. (Like a new baby being around.) Training also helps you to de-code your dog’s behavior, so you can tell what she’s going to do.
If you and your wife (I guessed here, didn’t check your profile, and don’t know your gender) are not 100% sure of your dog (and if you were you wouldn’t be posting your question here) and both of the baby’s parents are not 100% comfortable with the baby being around the dog, don’t let the dog around the baby. Odds are in your favor that nothing will ever happen, but they were also in Holly’s favor, and that didn’t turn out so well. (Holly, I’m not down-playing your experience in any way. It was tragic, and I’m sorry for you and your son.)