Ok, I know I'm probably going to be the only on here saying this... but he doesn't really NEED the milk.
The only vitamins he really gets from milk are calcium and vitamin D. The other thing milk offers is fat. All of these are available from other sources.
Vitamin D can be purchased at any drug store in liquid form. I give it to my daughter daily in the fall and winter months because there just isn't enough exposure to sunlight for our bodies to produce the needed amounts of vitamin D. I take it as well.
To get the calcium, there are many sources. Papaya, broccoli, kale, various beans, etc... You can find sources that are easily fed to a 1 year old, plus you'll be introducing lots of new foods and expanding his food choices.
Fat: Cod Liver Oil. Nordic Naturals is one of the best brands of Cod Liver Oil. This has all the essential fats kids need for their growing brains and bodies. Nordic Naturals even has some that also has the addition of Vitamin D. :-) It comes in different flavors... like peach, strawberry, lemon, citrus. I've been giving my daughter a daily dose since she was 13 months old. She loves it.
With a little thought and ingenuity, you can avoid milk products until your son can tolerate them. Then, you can add things like yogurt and cheese. Milk just isn't necessary.
In my opinion, pediatricians push this because most parents aren't willing to look at the alternative options to provide their kids with the things milk provides. They want a 'one stop shop'. In reality, the milk we drink today is NOT the milk our grandparents drank which did have many health benefits. Today, the pasteurization process and homogenization process strip our milk of all the good nutrients it used to have... which is why milk is called 'fortified'. They have to add some of the nutrients back into the milk. Anyway, I'll get off my soap box.
I hope I offered some alternatives that can work for you and your son. :-)