Offer her something else. Stop buying so much milk if possible and try and coax her to drink squashes or fruit juice. Let her come shopping with you and choose her own bottle of squash or juice that's only for her. Get her to make her own smoothies and see what she likes. Help her make her own freshly squeezed orange juice. If children can help making things they're more likely to want to consume it.

If its the fat content you are worried about, try soy milk, its healthier in a lot of ways to drink all the time