I have to make this brief since I am late getting out of town for a few days. A vegan diet can be one of the best diets in the world or it could be one of the worse. Let me explain. If your daughter eats a junk vegan diet it can be dangerous to her health. On the other hand if she eats a well balanced diet you should see an improvement in her health. Yes, she will loose weight but it should not be dangerously low. If she gets too thin than there is a problem. She may be eating a junk vegan diet, which is even worse than a junk meat diet, or she has another problem. Please have her read books on a good vegan diet. There are many out there. She could also go to: for a lot of good information. They have VEGAN Mailing List, VEGAN Resourse Library, Doc's Blog (mine), and other valuable information.
You are the parent and even though you may disagree with her choice of diet, you can still make sure that she eats a well balanced vegan diet. Do not allow her to eat a junk vegan diet. At her age it could be dangerous to her health. Be as alarmed as you would be if she ate a junk meat diet. Both are bad for her. Insist that if she eats a vegan diet that it must be a good vegan diet. I hope that this helps and I am sorry that i have to run. I am already late.