I hope my response doesn't come across the wrong way - I really want to try to help.
But, is she waking too early for you or for her?
It sounds to me that she's waking with her natural circadian rhythms which are different for everyone. Our son (3.5) can go to bed at 11pm, and he still wakes-up at the same time every morning. Our daughter (2) would sleep until 9:30am if you let her.
We keep the blinds open in both kids rooms as our son's developed a fear of the dark.
I don't think your idea of having an alarm tell her when she can come into your room is bad - but what if she's afraid to come in when she really needs something? Like during potty-training if she's had an accident.....will she just sit in the soiled clothes?
My husband and I would take turns when one of the kids got up early, we'd go into the family room, get out a blanket, put one of their shows/movies on (basically without volume) and rest in there with them so the other parent could sleep as much as possible.
If it were my child, I'd probably just get up with them and enjoy the time together. My kids are 21 months apart, so I know what it's like to have 2 little ones and the demands of each - the difference is I was going through chemo from the time our daughter was 10 weeks until she was almost 9 months. So, I had to balance side effects, a job, and 2 little ones - each moment with them is a gift (even if it's a really early morning gift when you'd rather be sleeping).
Good luck.