Wait! Wait! Not so fast ...
As I understand it, the question you asked is whether you could justify getting a neat new reader for yourself by explaining that you only reason for doing so was to offer your child a reader of hers

.
Now personally, I would never do such a thing. My kids really did need that TV for the rec room, and the computer too. I selflessly gave up both my main TV and computer to help them out. But of course, I found myself without the required equipment in my family room and I just had to buy new (better) ones. But enough about me.
Can you afford a new reader? Are you sure that the new Sony Daily editions reader with 3G wireless and a bigger screen won't tempt you anew when its released? Are you comfortable with the screen quality of the 600 -- some people feel that it is not as sharp as the 505, but others are quite satisfied with it. Then I'd say go for it.
In my justification of a reader for my son, I realized that we enjoy reading the same books. To the extent that DRM allows us to share ebooks, the cost of a reader is easily justified. I'm getting him a $200 device, and if I can forgo the purchase of 20 to 25 books by loaning books between us, then I will have paid off the device.
I assume that I can provide him with a note that explains to his teacher that this is a book, and not a game device or a computer. We'll see how that works.
My biggest concern with my son, and any youngster is durability and potential loss/theft. E-ink screens today have glass substrates. Dropping them can lead to cracked screens. I'm not sure how they will stand up to teen/pre-teen lockers, backpacks, and running between classes. However, my son has had a cell phone for three of four years now and he has yet to loose or break it.
I guess you could treat this the other way around -- as a test to see whether she is eventually ready for a cell phone. At least it doesn't have a price plan.
On another subject. Have you read the Twilight series yourself? I haven't, but my wife has. She says the first one is a bit more circumspect, but as the series goes on it becomes more explicit in its relationships. Depending on the level of maturity of your daughter, you may want to skim through the other novels before she dives into them.
Good luck!