AGE:
If this were my child (I have a 12 yr old boy and 8 yr old girl) I would shave them now, if it were such a big deal to them. I agree with Laurie A. below. I don't think there is a "magic age." I don't think you are a bad mom for waiting longer or starting now if you see fit. You are not doing this for your ego or fame (TV show). You would be doing this to help her feel more comfortable socially.
I'm sure she is perfect head to toe to you and any sane adult, but if she is feeling so self-conscious about it (and being teased and bothered about it, I'd help it out.
Or you can help build up her confidence. That's another way to go.
METHOD:
I never used Nair on myself and would not on a child.
I always shaved as a teen and still do sometimes because it's easier.
You can't escape in the infrequent cut. That will happen.
Waxing is awesome BUT it hurts a lot. I wouldn't subject a child to waxing unless they were 100% OK with that, and I would imagine that would be in teen years.
AVOID:
I would avoid Lasers. I had a sample done to my underarm in my early 20s and I felt it hurt a nerve that went to my nipple! It felt numb for a long while. Too freakin' risky. (There are horror stories online of laser removal.) If she's an adult and she wants to do that to herself, that's her choice, but I would not do that to someone under the age of 18.