Cow's milk for humans is something that not even all doctors agree on. My mother works in an assisted living wing of a retirement home and she is constantly telling me about doctor after doctor who pull milk from their patient's diets. One is a cardiologist who won't drink it himself because he says it's so unhealthy.
Having said that, there is also an ethnicity issue. If you daughter is anything other than caucasian, she may be lactose intolerant. There is also another thing (the name of it escapes me right now, of course!!!) where drinking milk can cause iron to cease to be absorbed and cause anemia.
I wouldn't push it. You can get calcium from broccoli, fortified OJ, etc. And vitamin D comes from the sun!
Here is a nice site that lists out foods that you can eat that give you the nutrition milk offers if you don't eat dairy:
http://www.bchealthguide.org/healthfiles/hfile68e.stm
Also, sometimes kids just go through phases where they don't like things for awhile. My daughter loved broccoli all her life and then thought it was disgusting for 6 months. Who knows why? Maybe she ate a piece that tasted strange or she had a tummy ache afterwards once... I think we all have instincts about avoiding foods for certain reasons sometimes even if we can't explain it, just like we have cravings at others.
Personally, I wouldn't push it. And on another personal note, I didn't give my daughter cow's milk until she was 4 because I was trying to prevent dairy allergies. I gave her soy milk instead. I have since heard that there may be problems with giving soy because of the pseudo-estrogens, but have not done my own research (my daughter is 6 now and drinks milk just fine- although I do buy organic because of the growth hormone issues.)
Hope some of this helped. I'm not the most informed person on the topic, but I thought I would throw out there what I knew and had heard. Google it if any of it interests you further! :)
-Amanda