We gave the books to DD8 to "read" until she fell asleep as early as 18 months. I have a picture of her when she was 2 lying on her bed with a giant disney book open and over her face!
MON-DD8 has pretty much the same sleeping strategy as your daughter. During the school year it's in bed at 8:30.
After we close the door......what happens in DD's room, stays in DD's room.
I find it unproductive to police her sleeping. I figure she will go to sleep when she is sleepy.