What my understanding is with milk is that dogs are not able to digest it. I would not give it to your baby.
I would though, start free freeding a high protein, grain free, kibble to your little one. I am not familar with the raw diet feedings. However, since you are working most of the day, make certain your dog has free access to the food and water. Kibble is safe to be left out, with no problems. Find one that he really loves to eat.
I am thinking others on YT can give you more advice about the Raw diet feedings when your home, and you can still feed him that too w/o any problems. I went through the same thing with Suzi. I did not know that she was too thin , with all her hair > However i had her clipped, then I saw that she was thin, and felt terrible. She had energy though and never behaved differently. I did not like how she looked though, not the cut, just that she was thin!
This is when I began feeding her more canned food, and it has the high protein that she needed. Since than she looks so much better and beautiful, and stronger too! Anther thing to keep in mind, is that if your Dog was to become ill, it will be a lot safer for him to have the extra protein and heavier muscle to fight off illness then if he were a thinner, weaker dog. This is also true for humans.