A., It sounds like you are doing a great job! I would stick with what you have and just work with your daughter to stay quiet in bed and teach her to fall back asleep. It is a great skill to know. I am the sleep Nazi mom. I have never allowed my children to get up before it has been 11-12 hrs after their bed time. But this does take some conditioning, that is well worth the results.
First is to keep the room dark, try the darkening shades or curtains they work really well!
Also consider putting them to bed just 15 min earlier and see if she sleeps longer. you could gradually keep moving it up till she wakes up when you want her to.
The main thing that I do when my kids wake up to early is go in and comfort them. It might sound funny, but I make sure that I look tired, whisper and not open my eyes all the way. Saying something like,
"it is not time to get up yet, it's still sleeping time. Mommy, and Daddy and baby are still sleeping".
Depending on the persistence of the child, you might get them to lay back down and go to sleep. Or you might have to say,
"we are still sleeping so you can sleep or you can look at some books in your bed quietly and then sleep".
Make sure they are not your favorite books, because some destruction might occur.
It also helps to have a visual like a clock, I put tape on the time that they can get up at. If they wake up and the hands don't match the clock, they get to go back to sleep.
You could also do a reward system, that if she does lay quietly until it is time to get up, or look at books, or go back to sleep, she can earn something fun in the morning. A small treat or a fun activity, or points for a bigger reward.
Good Luck
E.