R.R.
Pasteurized, homogenized cow's milk dairy from cows that ate who-knows-what does contribute to allergies, infections, and mucous problems for many people. You are a lot less likely to have issues with cow's milk if it is from grassfed animals and is not processed, but fresh (raw)- if you can find a conscientious dairy with high standards (and legal ability to sell it to you).
NO, soy is not the best alternative. It contains estrogenic properties and is goitrogenic (depresses thyroid function), so you certainly do not want to give a lot of it to a baby. Soybeans are the hardest beans to digest, and all the processing that goes on to make them into dairy substitutes (as in soy cheeses) make them less of a whole food and more of a processed food. Soybeans are highly GMO (genetically modified) and so soy should only be consumed if its organic. Soy is best consumed fermented and in smaller quantities- miso soup, nama shoyu soy sauce, etc. It's not a bad food, but there are better choices for a baby.
Goat's milk yogurt and goat's milk have been wonderful for my kids. They have never had illnesses that required prescription meds or even over the counter ones... we think all the probiotics in their regularly consumed goat milk yogurt has been phenomenal for their immune systems. Goat milk is alkalizing (cow's milk is acid forming, or more prone to causing mucous), has smaller easier to digest proteins, and is naturally homogenized so artificial processes are not required to keep it from separating.
I think a little dairy is fine if he is still breastfeeding, my one year old nurses a lot and enjoys goat milk yogurt once a day with a meal. He will also sip on fresh goat milk occasionally. I think signs of too much dairy would be excess mucous or allergies.