I know this will probably not be a popular answer, but try adding ovaltine or nesquik to the milk. If your child is not allergic to milk products, then I think adding something in to help convince her to drink it is not a bad thing. My doctor (as well as my husband who is also a doctor) told me that it is important enough for them to drink milk that if we have to add chocolate (or strawberry) to the milk to get thm to drink it that it is ok. Both our girls had chocolate added~ we just chose not to give any extra calories elsewhere like in juice, so that we were not giving her too many calories in a day. Both of my girls are VERY healthy and are by no means overweight. I know that many people are concerned about sugar with their children and I was too. But I just decided that I would not give them juice and would add the mixes in so that they were getting their milk. I provided water as an alternative as well as the 10 calorie koolaid that I would put in their sippie cups~ for a treat every now and then.
I hope this helps! Nursing is wonderful(I did it for a year with both of my girls), but unfortunately, we can not do it forever and they need nutrition elsewhere~ do what is best for your little girl. I hope this helps!