When I was about 6, I really wanted to take gymnastics. So somehow my parents managed to put me into a class. But once I was there, I was TERRIFIED. I didn't know anyone (I was always very shy), I didn't know what I was supposed to do, or what was expected of me. I freaked out and bawled my eyes out and begged my mom to not make me go out there and do the warm-ups with the other kids. She MADE me. I cried all through the stretches. And you know what? I was fine. I learned. I adapted. I had fun. And the next few classes I felt more and more comfortable. My mom was not a perfect mother by any means, and I hated her for this at the time, but looking back I know now that she did the right thing in making me get out there out of my comfort zone a little. If she had let me stay in my comfort zone, I never would have done anything but read in my room!
I think your daughter is too young to make the decision for herself whether or not to quit. It's okay to tell her that she needs to stick it out for a few months, that she participate with the class. Go around the corner for 10 minutes so she can't see you. If, after a couple of months, she is not getting more comfortable, then perhaps reevaluate.