This is my take on it (and I've been a lactose-intolerant pescatarian for quite some time)...
You can allow her going veg with the understanding that she must work with you to maintain a nutritious diet. This will mean trying new things. Be glad she's not going vegan, because that would be a mindblowing amount of adjustment... :)
It took me a while before I decided to try Tofurkey products, because my palate was accustomed to meat tasting like meat. Meat substitutes don't have the same texture or flavor, so she needs to know that some of her alternatives will take some getting used to.
My suggestion would be that when you make up a veggie entree--say, a tray of black bean enchiladas--have her get involved as much as possible. Teach her how to rinse the canned black beans (not so expensive and beans are a great protein) and how to season them to her taste. Make a tray of them and then after she's had her dinner, have her help to freeze the rest in containers so that you have an instant meal for her on some of the meat-heavier nights.
Help her to learn which foods offer healthy proteins. Also, be wary of her consuming too much soy. This isn't good for developing girls, just as dairy with hormones can cause precocious puberty... balance is important. I say this because a lot of the frozen meat alternatives are very soy-heavy.
Help her learn how to make scrambled eggs/hard boiled eggs. This is a better protein than just eating lots of cheese/milk options.
One family I nannied for had a child who began being a vegetarian when she was about nine. They had quite a journey in figuring out how to ensure good eating and nutrition for her, and this eventually included making her responsible for educating herself on the subject. She's going off to college this month and has been strictly veg for the past 9 years, and is a very healthy young lady. So it is possible-- but you may need to hold her feet to the fire from time to time to ensure that she's doing this properly.
Here are a couple articles:
http://parentables.howstuffworks.com/chow/vegetarian-nurt...
http://www.amazon.com/How-Cook-Everything-Vegetarian-Meat...
And I'd say this: if you do join her and go veg, remember that your stomach will stop producing the enzymes necessary to digest meat at some point. Which means that you will have to endure getting sick (basically) to get your "meat-stomach" back, so that your body will produce those enzymes again. I love my buddy's ribs, but now realize that more than small bite or two and I'm going to be feeling pretty bad later on. Just a caution...