First of all are you giving her whole milk? It is so filled with fat that some children just do not like the taste of it. My son has always said it is like drinking cream. He has always drank skim milk and since he likes cheese, yogurt, cottage cheese, etc. his doctor has always said he is getting enough fat. Children do not need a lot of extra fat.
Another thing you can try is soy milk. Soy formula is closest to breast milk so she may like soy milk.
Another choice is goats milk. Goats milk is already pasteurized and children have less chance of an allergic reaction. You know she is not allergic to milk if she is eating other milk products.
You can always get the vitamins from fruits and vegetables. Do some research on the internet and ask you doctor for some suggestions of good books.
As long as she in not allergic or lactose intolerant there is ways to cook with milk and she will never know. Example: Does she like pudding? Make mashed potatoes with real butter and milk (not substitutes), Put butter on her sandwiches, if making soup try making a cream soup and so on.
Do make sure she gets her daily vitamin. Our son likes the Ester-C (Raspberry), it comes in a little packet and you mix it with water and it turns into flavored water (or as our son says it is like a spritzer.)
Wish I could have been more help..
S.