I wouldn't get one for my kids at this age. My husband just got me a Kindle Fire for Christmas, and while my kids (ages 7 & 5) have enjoyed playing with it (they've discovered the apps, especially Angry Birds), I wouldn't want them to have their own, because of the risks involved. Your daughter may be old enough to be more responsible, and understand that some books and apps cost money, but my kids don't understand that, and I'd be worried that they'd accidentally download expensive books or apps just because they didn't realize they cost money. Also, there is a web application, and you can download a Netflix app so you can watch videos on your Kindle, and there is an Amazon video and music app, so you can purchase things like that, and again, I'm afraid they'd end up spending money without realizing, and/or watching something I don't want them to watch, but I wouldn't know it because they're playing quietly in their room with it.
But, you also have to think what she's going to read on it. Are you prepared to get her not only the Kindle but also books to go with it? Sure, there are a lot of public domain or free books (the original Wizard of Oz books are all public domain), so she can read those w/o paying for them, but many other books you'll have to purchase, and you can't borrow them from the library or purchase them used on your Kindle, which would be a consideration to me (although you may have more money than I do).