We went through this with our son about a year ago (we're vegetarians). You'll eventually have to move away from formula, but unfortunately, most nut or soy milks lack the fat that your growing baby needs. If you do opt to go for a non-dairy milk, be sure to do a lot of research and talk to your ped. You will need to supplement additional nutrients and have base your meals/snacks more on healthy fats, such as peanut butter, avocado, etc. Dairy milk has a lot of vitamin D and calcium as well, and while most milks are now fortified with it, it is something you need to pay more attention to.
We eventually decided to switch our son to organic dairy milk (and not commercialized organic, we purchase milk from a farm-coop so we know it's really organic). Our DS really didn't take well to almond or soy milk... if he had, we might have gone with one of those and supplemented fats into his diet. We're hoping as he grows older, he'll switch to a vegetarian alternative.