Different circumstances here, but we just had our first (only!) child and he will be 6 wks tomorrow.
We had everything set up long in advance so not much was really new to them after awhile. This way as things were added, there wasn't suddenly a big massive change for them to notice. Life just went on for them.
When we brought him home, we let the smaller more gentle females meet him first. Everyone met him individually and with both of us present so one could handle our son and one the dog. The girls have both been around babies quite a bit over the years, so there was no concern with them other than ensuring they remained calm and gentle around him.
We waited to introduce him to the boys for several reasons. One, Micah was adopted as an adult so we had no real knowledge of his kid experience, much less babies. He lived in a 10 x 6 ish pen in the backyard at his former home for 2 yrs. No socialization. Kodii lived with kids, but not babies, and was still in recovery from a total hip replacement. Due to constant confinement on leash, in an exercise pen, or crate, he was pretty hyper and we didn't want him to inadvertently harm our son. We knew he wouldn't be aggressive, however.
With the boys we allowed them to see him only at first. No sniffing except from a couple feet away or through a crate. They had to learn to remain calm and not get excited and overly curious about him. So once they remained calm over a week or two of time doing this, I allowed them to come up and sit by me and sniff him up close while I held him. That's all they get to do, and all they need to do IMHO for now. They don't need to do anything more than see him, hear him, or smell him.
We don't allow licking of the baby although occasionally Akira sneaks in a quick lick on the foot or something. Akira and Audrey are safe in the house with him. They know he's a little person and to be respected, they know not to step on him if he's on his playmat on the floor, etc. The boys are FAR too rambunctious for this, and we utilize gates in the house to seperate them from where he is. They can still see and hear him, it's an open concept floorplan so they aren't relegated to a room by themselves or anything. They just don't get to be directly with him right now.
Safe as they are (the girls anyway), never leave your dog and baby together. He goes where I go in the house if the dogs are loose.
I would be rather concerned if I were you, and would start taking my dog around kids constantly although I wouldn't allow some strangers kid to approach because your dog is displaying either aggressive or fearful behavior (hard to say without seeing the dog and action). you don't want to use someone's child as a guinea pig!
I would start using lots of positive reinforcement when around kids, and strive for calm quiet behavior. Work your way closer and closer to the kids as time goes on. I would not count on the dog bonding with "your" baby just because it's yours. A lot of people assume this will happen and that's not always the case. Family dogs all over the country bite their own kids, and yes, at times unprovoked. Train, socialize, and keep your child safe.