As mentioned, many babies are vegetarian and vegan, and grow up just fine. You can get protein from plenty of other sources..beans, whole grains, etc. Even Dr. Spock recommends a vegetarian diet!
As for the brain development issue, the key nutrients important for young babies are Essential Fatty Acids, found mostly in nuts, oils and flax (in a vegan diet). However, if you're still breast feeding or using formula, there will be EFA's in there as well.
The ones I pity are the ones who never stick out their neck for something they believe, never know the taste of moral struggle, and never have the thrill of victory. - Jonathan Kozol