We had had our dogs 4yrs before we had DS1 and although they were good with kids out & about, there were no children in the family to gauge their response. The are both rescue collie-crosses.
we started by stopping them sleeping in our room and making them sleep in their beds in the kitchen (i was about 6months pregnant at this stage) - they are allowed on rugs in our room during the evening but it just making sure they know the pack structure. also feeding them after we had eaten.
when DS1 was born, a friend took them and brought them back once me and DS1 were settled on the sofa. I held DS1 and let them come to greet me and sniff him. It was no big introduction - DS1 was asleep. They were a bit shocked by the crying but they had their beds as a retreat.
Did the same with DS2 and they have accepted both boys.
I dont have a kitchen door but a tall "dog" baby gate so the dogs are safe from my toddlers but arent excluded from the house. We have lots of walks with the pram and they are very protective about strangers coming up to the boys - not aggressive but just stand between DC and the stranger. They are also excellent hoovers when weaning.
Having said that, they are never left alone with DC as much for the dogs safety (my younger dog as a very pullable tail) as the boys. The children arent allowed to touch the dogs when they are in their beds or eating - the dogs need their space.
It seems to be working well. We do have grumbles rather than growls when the dogs have had enough of the noise/being played with but I know my dogs and their limits and they trust me enough to know that I am going to intervene and remove them from the situation. I think its about reading both dogs & childrens behaviour and being sensible.