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I think that a long as the baby is nursing on milk, there is not that much difference in the nourishment that is received from the milk of a different species.
As humans, we use milk from cattle, goats, sheep, and even camels, all of which are vegetarians. Yet their milk has all of the required nutrients for humans to use it even for infant formula.
I have had dogs that nursed kittens and raised them, and it seems perfectly likely that a dog, or even a wolf, as @Thor mentioned, could nurse a human child and it would survive, as long as it was getting as much milk as it needed.
The difference would come when the child (or whatever infant) was old enough to eat food, because then the diet might be limited to whatever the parent species ate.
Different digestive systems are designed for different diets.
For example, a cow can grow to over a half ton by only eating grass, which would not sustain a dog or wolf, because they have a totally different digestive system.
It seems like many animals have a tendency to want to help any babies, even when they are from a different species. Dogs, especially, are very protective of children, and will give their own life to save children who are in danger.
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