A.H.
I am a firm believer that children should eat what the adults are eating. My son was always fed what I was eating with each meal (with the exception of really spicy food). He now eats everything except tomatoes. Children will not starve themselves, I promise. I would personally switch your daughter from milk to water. Milk (even organic milk) is full of growth hormones that are designed to grow a baby cow, not a human child. Calcium can be obtained through many other sources, including green leafy veggies.
Children only end up being picky eaters when their parents allow it. I went to China in 2003 when I was pregnant with my son. The chinese people eat a diet that is mostly vegetables, meat and rice. I asked a local Chinese woman if she knew anyone that didn't like vegetables (since it was a huge portion of their diet) and she couldn't think of a single person, not one! Now think of how many children and even adults in the USA that don't like vegetables.. It's 100% cultural, if you don't eat veggies in China, you don't eat. If you don't eat veggies in the USA, you parents give you chicken nuggets.
Some of the other responses think that her pickiness is related to your daughters extended nursing. I think these people have hang-ups about extended nursers. My son also nursed until he was 3 and never had a problem transitioning to an all food diet.
In response to what another woman wrote above me.. I DO NOT think that you should HIDE healthy foods, ever. Once you start hiding the healthy foods kids gets the idea that we expect them to think healthy foods taste bad. Kids live up to the expectations of the adults around them. They are more influenced by what they think they're supposed to eat rather than what they actually like. My son gets full servings of all veggies, including things like kale and meat in every form (appealling or not).