What's her reasoning for wanting to go vegan? How well thought out does it sound? How willing is she to learn about and implement vegan nutrition?
Honestly what you are describing right now strikes me much more as disordered eating than veganism. Vegetarianism is a common cover for adolescent eating disorders.
HOWEVER, I'm not in the situation and you're in a much better place to assess is she's deeply committed to, say, animal rights but just extremely picky.