My 10 year old daughter has decided she does not want to eat meat. Should I offer a protein supplement to her?

It's hard to find a natural plant based wholefood without protein.

Good vegetarian sources are quinoa, buckwheat pasta, hempseed,  lentils, nuts and seeds, chlorella, Tofu, poppyseeds, brocolli, peas and beans.

Use it as an opportunity to encourage her to eat a wider variety of foods and less processed foods

Right on, Tony!  The whole protein thing is out of control in America.  You don't need the levels of protein that bodybuilders use.  All those protein whey supplements clog the lymphatic system and can damage kidneys with an overdose of protein.  Also, as Tony mentioned, there are plenty of whole foods with all the protein one needs, especially a young girl. 

I don't eat meat and am a pretty hardcore athlete.  I mountain bike in the rugged Arizona desert terrain, 50-100 miles per week and lift weights at the gym a couple times a week.  I have found that complex carbohydrates are more important than protein and should amount to half of the calories consumed each day. 

For more about that, read my article:

Natural foods provide complex carbohydrates that are essential for health