I agree with the others as far as fasting.
As for the vegetarian part of your question, we're Catholic, and my husband, 14 year old son, and I gave up sugar, caffeine, alcohol (not a problem for our son ;), and meat for lent. My husband and I still eat fish, but my son doesn't like seafood, so he's basically been vegetarian since lent began, in addition to no sugar (well, as little as possible - sugar is in EVERYTHING - it seems that way, anyway) or caffeine.
We get our protein mostly in beans. Beans, beans, beans - we eat tons of beans. We also eat a lot of nuts. Honestly, we all feel a lot healthier since we started this, and will likely continue this after Easter. It has certainly been a sacrifice, as lent should be. Man, I want a Dr. Pepper! But, we all agree that feeling healthy is worth it. Getting rid of the red meat and the sugar seems to be a big plus.
I'm anemic, and always have been, so I take vitamins, as well.
If your daughter is truly doing this for religious reasons, and not some fad diet, I would support her completely as long as she can do this in a healthy way. My son does fast on Ash Wednesday and Good Friday, but that is one day at a time. Good luck to your daughter, and good for you for getting more information!