I'm reading the series to my own DD6 as bedtime reading. We're on our third one right now. We just finished watching the full movie series this past weekend, but she has always been reading behind what she has seen on the screen. This means she has already been exposed to the scary bits, so she knows how she'll handle it, and she already knows how it'll turn out when we read it.
One huge advantage to doing it this way is she notices how different the book experience is from the movie, which reinforces how books are superior to movies... not a bad lesson to learn at such an early age.
I occasionally stop reading to ask her questions about how she's following along. It's pretty clear that she's not thinking deeply about the reading, because she's six, so she's just sort of allowing the story to lead her along... which is fine. But it's also clear that she's keeping up with the story and the characters, so no worries there.
