I don't have any kids, but my daughter should be making an appearance in early April (getting kicked in the sides as I type).
In my personal case I think I'll have NO problem with my dog around the baby. I have what may be THE most laid-back sweet passive tolerant dog EVER TO HAVE BEEN BORN. Seriously. I've never known a dog like her. There was a puppy who would not stop humping her one time, and it was, like, hours before she finally sort of pushed him away with her mouth (seriously, it wasn't a bite or a growl or even a snap, but more like, "GET AWAY FROM ME ALREADY!"). I can give her a bone with meat on it, and she'll be happily gnawing away, and I can come up and pull on it and tease her and she will just look at me all sad like, "can i have that back please?" Or she'll just get up and go to the other side of the room.
She's been around my friend's 10 month old, and she just lets him hang all over her, and stand up and grab her neck fur and look her in the eyes. She licks his ears

he had a bit of food on his head one time, and she licked his head forever, and he just giggled and giggled.
It's just SO nice to have a dog whom I trust 100% to not purposefully hurt the baby. The ONLY concern I have with her is that she's about 35 pounds and has no concept that people don't like to be stepped on directly. She'll just walk right on you. So we'll have to work with her on that a bit.
The cat, on the other hand, may be a bigger issue. He'll ignore the baby for the most part, but he is not a fan of them, and may swipe at them if they get too close. It's not really an issue until they get mobile... otherwise he just watches from a distance while flipping his tail around.