I would give it too him! I gave my son goat milk (the powdered kind) at around 4 months, but I continued to nurse. He wasn't gaining weight with my breast milk so the doctors told me to supplement with preemie formula. I did not want to give him formula, as I know many babies don't do well with it. Cows milk is just too hard for them to digest. Anyway, my dad has intestinal cancer and since he was diagnosed, my parents have been on the raw food diet. It talked a lot about how if you can't breast feed that you should give your baby raw goats milk (in otherwords fresh from the goat) and carrot juice which makes up for the rest of the nutrients that goats milk is lacking. Since I didn't have a goat in my backyard, LOL, I just got the powdered stuff at the store and continued breastfeeding and only supplementing enough so that he would gain weight. I figured the nutrients that goat milk was lacking, he would get from my breast milk. He liked it and we never had any trouble with it. He is now a very happy, smart, healthy, recently turned two year old. He knows all his colors, shapes, can count to ten and has been talking really well since he was 18 months. I would say he is doing just fine. I personally don't always trust a doctors nutritional advice. Most of them have only had a couple of hours of nutritional learning during their entire medical school journey. All doctors know is formula or breast milk, anything out of the ordinary (like goat's milk) is foreign to them. I would seek a Nutritionist or a Homeopathic doctor for more educated advice. I know that there wouldn't be any harm to give your 11 month old goats milk. By then he is practically one and then you would be giving him cows milk anyway. One month early isn't going to make a difference, espcially if your son is eating plenty of solid foods! I am sure he will be getting all his nutritional needs with the combination of both! Hope this helps!
T.