This is an excellent question, and there are many considerations to keep in mind. I'd recommend discussing this issue with your child's pediatrician
. First, there are other animal milks other thank cow's milk, and then there are the non-dairy milks (which do not come from an animal source).
The most popular alternative animal milk is probably goat's milk, but goat's milks is especially deficient in several important vitamins, such as folate, and consuming it in large quantities can lead to deficiencies in these vitamins.
Among the non-dairy milks, the most popular are soy, rice, and almond. Soy milk is the most accessible and it has the highest amount of protein. All three of these milk products are low in calcium and vitamin D, however, unless the are fortified appropriately, and this is something to be on the look out for. Additional, many of these milks contain a lot of added sugar, and this requires reading the labels closely.
Again, I'd recommend discussing this issue with your child's pediatrician. They know your child's medical background, as well as your reasons for wanting not to use cow's milk, and therefore they can give you more detailed advice on which might be the best choice for you.