How can I stabilize my 1 year old's wake up time?

[G and G]

My DD is a little over 12 mos now, and we have a good routine, but she wakes in the morning anywhere from 5:25am - 7am. It drives me crazy. Yesterday I had to wake her at 7am, this morning she was up at 5:25am. She is down to one nap, from 12:30-2:30, and goes to bed at 7:30pm. My pediatrician has recommended I keep her naptime and bed consistent because her sleep was ALL OVER the place.
It HAS gotten better, but the wake up time is still so very random (but at least not 4:30am which is was for a while).

Over the last week she has woken up at 6am, 6:20am, 6:50am, had to be woken at 7am, and 5:25am. I don't get it! I took her into bed with me and DH this morning and she did fall back asleep - Thank God! But that does not always work. I thought it might this morning becuase I knew she was still tired.

So a 'typical day' for sleep might be:

6:30am wake
12:30-2:30pm - nap
7:30pm - bedtime

If she wakes very early she get a catnap around 10:30 to make it to her nap time, which I then push to 1pm.

Any thoughts on how I can stabilize her wake ups?

[Diegos Mama]

How long is her nap?
Is her bedroom dark - ie is she waking with the sun?
Is she hungry when she wakes?

[Sarah - Enfys' Mum]

What I found helped here is that I will not, ever, (unless she's got a dirty nappy) get Enfys up before 7.  If she's awake and happy, I leave her alone; if she cries, I do wi/wo.  At 7 I get her up.  Unless she's still asleep (which has happened maybe 10 times ever) in which case I leave her sleep. 

[G and G]

Her nap is typically around 2 hrs, anymore than that, and it affects her night sleep.
I have room darkening shades in her room.
She is not waking due to hunger. She can wait to be fed once she gets up.
Most times she is happy when she wakes, and can entertain herself - some mornings only for 10 min, other mornings for 45 min. I just wish I knew why her wake ups or so random!

[Ryan&HollysMom]

we always left him unless he was crying. if he was we'd pick him up, make sure he's okay, whisper that it's still nighttime and put him back down. we were VERY persistent. sometimes i'd wonder why i'm doing this as i'd go in and put him down many times but it has payed off in the long run. thank god that worked. now he's 2.5 and will just call out "MOM" and if it's too early i'll go in and tell him it's not time to get up and he's fine with it and willl try and go back to sleep. good luck!!!