And with regard to nutrition - does she need to have milk if she is gaining enough nutrients from food?

The dairy industry has done a great job at convincing us that our diet is lacking in something if we don't drink cow's milk! Cow's milk is really just a convenient source of calcium and other nutrients - it's not required. There are many people in many parts of the world who do not drink cow's milk and still manage to get all the calcium, protein, fats, vitamin D, etc. that milk has to offer. Too much cow's milk in a child's diet can (1) put him at risk for iron-deficiency anemia (because cow's milk can interfere with the absorption of iron) and (2) decrease the child's desire for other foods.
After the age of 12 months (or sometimes later, depending upon your child), milk becomes a more minor part of your child's diet. If you have a child who refuses to drink regular milk and is no longer nursing regularly, you can offer yogurt, cheese, and ice-cream as substitutes. Also, you might put milk into various food products: pancakes, waffles, French toast, scrambled eggs, mashed potatoes, and baked goods. Added protein may be offered via creamy peanut butter and a well-cooked egg yolk; calcium may be derived from calcium-fortified juice or green vegetables.