The dog will let the baby do ANYTHING to her.
That's the way we kids were with our first dog Ginger, an English bulldog. She was the perfect Nana-type, including serving as my mom's baby monitor (pre-monitor days, in the mid-60s) and letting her know when my sister and I were waking up from our naps. Mom still marvels over that to this day, because she never taught Ginger to do that. She had no problems with us kids hanging on her/laying on her/whacking her back in our efforts to pet her.
Now, the dog we had as teens, Boots, was definitely not an infant/toddler-friendly dog. In fact, the one time my little cousin Bobby came over when he was about 18 months old, we ended up having to put Boots into the bedroom until they left because she got irritated by Bobby's fascination with her and got a bit growly (the only time she ever got upset with someone).