I started giving T a little cow's milk just before he turned one. We just started with a bit in his sippy cup at meals. I was still BFding then, but stopped around 13mos and switched over to milk in sippys only, and he did fine with the transition. But you can offer other kinds of milk as Jess suggested. Another option is almond milk mixed with coconut milk, which has a similar nutritional profile to cow's milk.
T is 2 now and he drinks about 2 cups of milk a day, sometimes less, and lots of water. Sometimes he gets juice, but we only really introduced juice around 18mos.