Hi, I was actually in the same position as your child, and neither my parents nor the school knew what to do with me. I was made to feel as though it was a guilty secret that I was bright, and told not to tell my brother (who was below average in his reading abilities) in case he became discouraged.
So I would underscore the point that you should encourage her, let her know that she is advanced. I understand the teacher's point about not turning her into a 'know it all', but this can go the other way (and this seems to affect girls/women a lot!), and she could potentially feel insecure in her abilities.
With hindsight, the most important thing, apart from encouraging your child to do activities which mean that she interacts with her peers (I ended up being very shy, as I would rather sit 'with my nose buried in a book' than interact with other people), I would recommend that you keep stretching her, and, although she is very young, try and introduce some structure and discipline into her day, which may be lacking currently, as schools often, as mentioned by another poster, leave bright children to their own devices.
Indeed, I was myself left to my own devices, so I would finish my work and then read some fiction that I wanted to read, or stare out of the window/daydream, and I think it's made me into a bit of a lazy, complacent adult. I'm 'successful', but I feel like I lack discipline, and have achieved results through last minute cramming and all-night essay writing sessions! If she finishes her work early, perhaps she could spend some time doing creative writing?
I know she's incredibly young, at 7, but I vividly remember what it felt like at 7, and I have a feeling that only reading novels is too narrow a horizon for your child. I agree that going to see plays is a good idea, and she may also be interested in art and art history, I know that I found these avenues exciting and interesting, when I stumbled upon them at around age 10.
Good luck, and you sound like a lovely mum!