Oh your DD sounds like my son when he doesn't get enough sleep and he is now 9 and a half..

We have to make sure he gets a minimum of 9 hours.. If he gets less (which is rare thankfully) he is a beast! he average 10-11 hours.. We put him to bed at 7 and he is usually asleep by 8 and is up between 5:30 and 7 most mornings..