Avid reading and comprehension do not necessarily go hand-in-hand. Some children can read well but a lot of the words may not make sense but they understand enough to move on and read the rest of the story. Does your DD ask questions when she reading a book about words she doesn't know? It is a good habit to get into. Maybe set a challenge to get definitions of five words she wants to understand in more detail per reading session.
I know this may not seem relevant but you could try her on some lateral thinking questions. That might get her to start thinking in that way a bit more. Do you read to her? If you discuss the stories that you read as you go along. Try and get her to think about what has happened, what is going to happen and what is unwritten but implied. Discussion of text is eye opening, I find that Dd often has a completely different perspective from mine which I am sure is a maturity thing.
I found my eldest's comprehension wasn't as good as his reading; what he focused on while reading was different from what was needed to answer the comprehension questions.
We read together quite lot and I would ask 3-4 questions each time, including inference.