Hi Mama-
Apparently, children like to be awake as early as possible to maximize play time. That's my theory, anyway. My nephew is 2.5, and while he sleeps for 8-10 hours, he never sleeps past 6 in the morning, ever. My sister basically tells him to play in his crib/bed until she comes to get him up. If he is hungry or has to go potty, he can say it out loud (they have a video monitor set up so they can hear and see him...it's tiny, but effective). So they will hear the ruckus of him jumping or tossing out his bedding or searching for a stuffed toy somewhere around 5 or 6 a.m. and he is perfectly content to stay there until 6:30 or so. They didn't put a clock in, but there is a sound machine and very light music playing (on repeat from sleepy time) that keeps him lulled for a bit.
I think that maybe instead of setting her on a time she can get out of bed, take the clock out of her room and tell her that at 6 a.m., mommy will come and get her up and she needs to wait. Invite her to read her books, play with her toys quietly in her room, go potty....even have a cup of water waiting for her (set it up in the evening) so she can have a drink, too....and maybe a snack (granola). It might keep her satisfied for slightly longer, and even though she is awake, it will allow you to get a little more rest. If that doesn't work, I say put in the effort to become a morning person (I am not one, so I understand how the early hours are a serious struggle for some people)...Who knows.
Good luck mama! And many hours of restful and uninterrupted sleep!
-E. M