In some ways, I think HBP is the most sinister of all the HP books. DH is more overtly dark, with scenes of torture etc, but it is always shown that this behaviour is wrong. The scene where Harry prepares to sacrifice his life in DH could be pretty disturbing for an 8yo, but equally it might be one of those things where it goes over a child's head.
HBP on the other hand has some less obvious problems. The depiction of Harry's relationship with Ginny is a bit... weird. I don't like the way the books handle Ginny in general, but in this book in particular, Harry's desire for her is presented in a very 16yo boy way, and it's not very well dealt with in my opinion. The language used imo is less than ideal, and I'm not sure if it's ideal for an 8yo to be reading. There's no overt sexual content though. I think part of the issue is that JKR can't write romance very well.
The violence in this book is also a bit more realistic, not just fantasy violence. For example, Harry casts a curse on Draco which has a similar affect to knife violence could in real life. Early on in the book, there is also a section where Draco discovers Harry spying on him, and stamps on his face and leaves him hidden on the train.
Some of the "memories" of Voldemort as a child are also a bit disturbing, but again, I don't know if these would go over a children's head or not.
I think OotP is dark in some ways, but it's still very much presented in a fantasy way- it still reads like a children's book to me, whereas HBP didn't feel like a children's book to me and it deals with fairly adult themes.
In all honesty, if you haven't read the last two books yourself, I would read them before deciding- only you will know what your DD can cope with.
I think HP is a really difficult series, because it almost grew up with it's first readers- I would say the first 3 books feel like definite children's books, books 4/5 feel more like YA books, and then books 6/7 read more like they were written for older teenagers/adults.