J.W.
I am a morning person, and so is my younger daughter. Even as a teen I'd get up before the crack of dawn -- 4:30, 5am, feeling ready to go. I love the mornings. My older daughter hates the mornings. The younger one is like me. But yes, that means we need earlier bedtimes. So be it. That's just the way we are.
But as far as not falling asleep easily, that's tougher. We had rituals with warm baths, story time, back rub, prayer, etc. The younger one, when she had trouble sleeping, liked soft classical music, but could not sleep DURING it because she loved it so much, but it emptied her head and relaxed her, and she fell asleep after.
Some kids do better with "white noise" and some hate it.
Plenty of active play during the day can also help kids fall asleep. No sugary foods... you know the drill - stuff you are probably doing right anyway.
Here is an article, maybe you can get some tips that will work for your little one. http://itsnotmental.blogspot.com/2009/01/sleep-timing-of-...
Lastly, consider how she acts during the day. Is she OK? Cranky & whiny? Let that help guide you.