I love animals and had dogs and cats living with my family. When I had my first kid, my wife had a large dog (a mixture between a labrador and a german shepard, and probably others - she found it as a puppy attached to a rope in the forest, left to die).
The dog was extremely quiet, socialized and what not. When we brought our baby from the hospital, he was really curious. We left him sniff the baby and the dog apparently understood that the thing that was brought in was important and decided to protect it (he was sleeping in front of the baby's room and would not let any stranger approach.
I had a similar case when I was a baby - my parents left me with their dog sleeping next to my crib outside and it would just do a "woof" without even waking up if someone would approach.
And then, one day, I left the dog alone with my son. My son was in that sort of cage made of ropes he can wander in and the dog was outside. I came back to the room and I found
... the dog licking my son face pressed to the ropes (unexpected happy ending)
I was really scared because it could have been something different (my childhood friend was bit to his face by his own dog, a normal one, not pitbull style but Great Dane IIRC). Nothing ever happended but still, this was this one time where it could have had happen and it would have been MY fault, not the dog's one.
I now have a cat. Well, my family has it, we just live together. The cat does not interfere with me (except sleeping on my laptop when I am not around) and is extremely found of my younger son (14 yo). I am telling my son to never get his face that close to the cat because she will a day or another scratch him (they are running and jumping together, playing). She scratched my leg once (and would not left from under my son's bed for that day because she was probably scared of what she did) - but that could have had been my face.
Accidents happen and animals are animals. This is not something bad - just something one has to be aware of.