Hi Megan - I dont want to sound too negative but I think you've bought into some of the hype regarding eating any kind of meats or milk. Consider buying an organic milk from a dairy that does not provide its cows with any hormones and separates any cows that might need to be on an antibiotic ie: Horizon or a local organic dairy. The same goes for meats like chicken, beef etc. It's alright if you choose to not feed your child these things but just consider the nutrient content of the plant foods you feed her to make sure her diet is balanced.
Also, you probably didnt get sick from eating meat for the first month because of toxins. When we stop eating meat, our bodies also stop producing the enzymes needed to digest it. It can take a little while for those enzymes to build to a point that eating meat doesnt cause stomach upset.
If you are choosing to not give your daughter milk, why does she need a milk look-a-like? Rice milk and soy milk are not milk. They are just products that look like milk so we dont miss the real thing. Soy products have a high estrogen content that can mess with little one's hormone balance. Also consider avoiding soy if you have any kind of family history of estrogen-related breast cancer. Rice milk has a very high sugar content combined with low protein so feeding her that product is setting her up for a glycemic overload.
You would probably be better off feeding her foods rich in calcium, protein and healthy fats rather than giving her fake milk and lots of soy. A kids multi-vitamin would also probably be in order if you change her diet to avoid Vit. D deficiency or anemia - talk to your doc about that one.
Hope that helps you!