Right, but my 9 year old has decided she's going to read the Hunger Games next.
. It's all about the individual child, and their maturity etc. (I would prefer she wait another year, but like her big sis, she's very sensible, and quite often starts a book, then decides 'not yet' and puts it back on the shelf for a few years.
Dd1 did this at 6 with the first six Harry Potter books. She read them happily, then picked up Book 7, started it, got a few chapters in, and decided it was too grown up, so put it back on the shelf. She decided to read it around 9, I think.
Certainly since then, she has reread an awful lot of books, and I assume got rather more out of them than her comprehension allowed the first time round at six.
however, she still read them and enjoyed them at the time.
All of mine were free readers by this point in year 1, to be honest. I was frustrated by the lack of age appropriate material for competent readers, but I have to say it's a non-problem, really. I solved it by allocating half an hour in the library and letting them come home with reams. Half of the books they read, half they didn't as they weren't what they expected / ended up not being appropriate in terms of ability, rather than content - too easy, or whatever. All of the suggestions above are great, and will be gathering dust at the library.
At six I would definitely steer of the newer young adult stuff (Hunger Games, Twilight bolleaux) but would also caution against becoming too ensconced in the nightmare that is the pink shelfery in the children's section in book stores. Libraries are pretty good about this, but I've seen book shops with v clearly delineated sections. There's only so many books on babysitting and middle school that you can read without your head exploding, once you have escaped the fairies and magic kittens.
I assume at six she's read all of the current little kids books - Cressida Cowell, etc.
Tbh, I've pretty much ignored what mine read past reception. It doesn't seem to have done them any harm! 
With my pfb, I did have a brief issue when she was 7, as they were giving her some of the much older Jacqueline Wilson's. They did adjust their policy, but tbh, in hindsight, I probably wouldn't have bothered if she hasn't been my first. No one wants a kid to have to deal with abused women, homelessness, truancy and whatnot at six or seven, but in reality, lots do. Better they broaden their horizons through the written word and not experience?