Thanks to everyone for your comments, even the very blunt ones, it's helped me get a better perspective.
For the record, it's not the hair removal that's worrying me, I'd happily show her how to remove hair safely, it's her extreme anxiety about body hair that nobody can see, and her feeling that if she removes it then she can hold back puberty. @GCAutist I think you understand.
She doesn't have any social media accounts, I've asked her if she's seen or read somewhere that she should remove all her pubic hair, or if her friends do it and she says no, it's just something that she does to give herself confidence. We have a very open relationship so I believe her.
Perhaps I should also have mentioned that she picks her skin on her arms until it bleeds and she sometimes pulls her hair on her head out, which added to my concern when I discovered that she'd been doing this.
I didn't snatch the tweezers off her and tell her off, I explained that she could have the tweezers for pulling any stray, visible ones out but that being hairy there is a natural part of puberty and that pulling them out wasn't going to stop it from happening.
After reading the responses I think I'll get her some gentle hair removal cream (shaving always makes me so itchy, that's the last thing she needs) and show her how to use it. We've discussed puberty loads of times and they do at school too, but I've ordered a book called "The Care and Keeping of You" which looks useful to look at together if she wants to.