My son doesn't start school until next Sept, but currently his reading is limited to spotting the initial of his first name so I doubt he'll be outstripping his teacher when he starts school (though I should add that I'm still achingly proud of him, as he had a very rough start in life medically, so to me he's a genius).
My point in posting however was that I was a naturally academic child, learnt all my spellings over night in Reception, galloped through books, that kind of thing. I went to a primary that was very mixed socio-economically, so we had some kids who got lots of support at home and some kids who were essentially neglected, one of whom I remember very clearly as he was incredibly bright but had a terrible childhood (and I now think probably ADHD, but that wasn't really heard of when I was a kid) and to be frank I'm amazed that the teachers (there were no TAs) managed to teach us anything at all really when they had such a mix of abilities and needs.
So, my actual points are:
Maybe the teachers can't deliver on their expectations of what your daughter could be doing because they have to meet the needs of every child in the class, all 30 of them, not just the bright ones. I think that in a nutshell is why some people choose to go private if they can afford it.
I can't ever remember being bored before about year 5 maybe, when we started doing whole class reading for things like history (very lazy teaching, hope they don't do that now) and it felt like a month to go round the whole class until I got to read my one line from the text book. I used to entertain myself working out which sentence would be mine. I doubt that your daughter is suffering from this at 6 and I'm sure teaching is a lot better now.
Finally, if you don't feel she's being pushed at school, just read and do stuff with her at home. My parents did this, stood me in very good stead, and it sounds like she enjoys reading and academic things so she should be happy to do it with you.
The main thing is that you say she enjoys school. I heard a R4 documentary on education a year or so ago where some academic suggested that you could basically stick the bright kids with lots of books and support at home in the playground for most of their primary education and they'd still cope fine from 11 because primary is all about the basics, and they'll just soak that up. I think that's an overstatement personally, but I do think that if your daughter enjoys school and loves learning she'll be absolutely fine.