My dsis is veggie, used to be vegan but she admits she couldn't hack it.
She did a hell of a lot of research, and I don't mean swallowing the propaganda from the likes of PETA or the multitude of pro vegan / animal rights groups - I mean proper research from independent, qualified dietitians.
She came to the conclusion that without devoting an awful lot of time and effort into her food that veggie was the best she could do without becoming deficient in one type of nutrient or another.
She explained it to me at the time and the finer points have gone out of my memory but in a nutshell most vegans (and many veggies) are deficient in some way or another it's just that the human body can take a hell of a lot of punishment and the effects don't show for years if ever, so they probably don't know that they're lacking.
Often the effects never show in an identifiable way that can be traced back to the dietary choices , it might just be that some ailment comes on years down the line that wouldn't have appeared otherwise (or would have appeared years later).
Your DD is a bit young to be doing that, she's still developing and needs correct nutrition. Personally I'd make her really convince me that she's done all the research on nutrition and knows her stuff. Again, I mean research papers, scientific journals etc... not the usual shit propaganda from the pro-vegan , 'meat is murder' extremists.
Just cutting out meat, switching to tofu and soy milk ain't going to cut it! I'd want her to understand exactly what nutrition she is currently getting from meat / dairy etc and show me what she's going to eat to replace those nutrients. Then I'd be monitoring her diet to make sure she does what she says.