To me I see a German Shepherd who wants to be left alone. Yes, he is being polite and indicating by pulling his bowl back that he really wants to eat in peace BUT how many times does he have to "tolerate" the interference of this child as he eats? He is learning that his food must be guarded from this baby. Dogs use their body to communicate with us. This baby is in the dog's space and not respecting the dog's attempt to be left alone. Over time if continued this will escalate especially once this baby is mobile. The dog is learning that the baby is a threat to his food and can not be trusted. Overtime this will lead to guarding behavior.
Watch the beagle. The beagle is showing concern about the baby. Taking a bite, watching baby, eating fast, watching baby. This dog is already indicating a threat and is very likely to be reactive if that baby crawls nearer to it's bowl.
Dogs should not be expected to "share" food or eat around small babies, toddlers or children. Leave a dog alone when they are eating is a oldie but goodie rule of thumb! Expecting your dog to enjoy the company of your baby while they eat is a disaster for all involved and setting everyone up to fail. This situation is teaching the dog/s that this baby is not to be trusted by their food and that their adults will allow this little one to take their food and crowd them during their meals..
Here are the steps.
1. While dog is enjoying their food in it's bowl I walk by and drop (while standing) a small bit of higher value (warmed up hot dog or chicken) without saying a word or stopping.
I repeat this walking casually by when they are on their bed, or enjoying a toy or anything they are focused on.
Many dogs will immediately grab the treat and then quickly return to the bowl never looking up. I repeat this until the dog begins to look up anticipating the higher value treat. As if to say"hey whatcha got?" Now the dog is anticipating and thinking approaching people could mean opportunity vs. ut oh...here they come again to steal my stuff!
2. I begin (over time) to expand the distance from the bowl to where I drop the treat. This challenges the dog to "choose" to leave the bowl to get the treat. Learning that it is ok and his food is not in danger of being taken by people walking by. There is no threat and no need to guard.
I repeat this step at different paces, with different shoes, crawling by, stomping by etc. Again, until the dog begins to look up happily at my approach as if to say "whatcha got for me?"
3. I then vary the location of where I drop the goodie to either by the bowl, in the bowl or a bit away from the bowl once the dog is happily looking up at my approach. Sometimes even toss goodie to the dog.
This allows the dog to see a person as an opportunity vs. threat around their food, treats, toys or special spots.
Guarding food is a common behavior and families with children must take this seriously. If your dog is demonstrating guarding behaviors such as: goblbing food quickly, freezing as you approach, displaying whites of the eyes as they look up at you, growling, body blocking their food or toys from you then you need to seek the help of a professional.