People milk can cause diarrhea, but formula is used up until 6 weeks of age after that grab a good puppy food. My fave brand is solid gold dog food it doesnt have fillers, it is holistic dog food no byproducts they use human grade foods to make the dog food.
I don't know about goat milk but cottage cheese worked for my dog... I would say anything with high protein content, but make sure they are getting plenty of exercise!!! And goat milk is high in protein so it'll help!!
Cow's milk is best.