Kudos to you for cutting out milk. My daughter was allergic to milk and breastfed, but she did not exhibit any adverse reactions when I had milk. PTL!
I can not speak first hand for the products but we buy the following for my daughter:
Tofutti mozzarella slices - They come in 'American' flavor too, but I've read that mozzarella is the least offensive. Personally the smell turns me off but she loves them. I figure this is because she has no experience with the real thing.
So Delicious ice cream - She likes just the plain chocolate and vanilla.
Purely Decadent - They sell pints of the ooey gooey ice creams. She used to love the cookies and cream but has become a purest and doesn't like anything in her ice cream.
They also make soy yogurt. I tried giving it to her on different occasions and it is not her bag. She is only 3 so I would not say she has a discerning palate and that it should be avoided.
Purely Decadent has also come out with coconut milk yogurt and ice cream. Both are more pricey than their soy counterparts. I think the only place I've seen them is at Whole Foods.
I am not sure if you need to avoid milk in other forms, i.e. whey and casein. Be careful with the rice milk and vegan cheese slices because they do contain one of the two.
Good luck!