At least get the rabies shot. Rabies is out there and it's fatal to you and your kids. In the 90's parvovirus was a common viral killer of dogs. So consider that one too.
I hate to be the one but large dogs should not be left alone with infants-toddlers. Even good dogs can have a bad day. It only takes a second for disaster.
That dog loves that child very much for him to just lay there and not move or push him away. He knows the child needs him and allows him to do whatever he needs to do. My dogs and cats did the same thing with my children and grandchildren as well. And protected them at all times.