My middle daughter (I have three) woke up very early when she was about 2.5 (and she shared a room with my oldest at the time). It was rough, as I am not a morning person! Anyway, we stopped her nap and that helped a lot during the night hours (she slept later) but she also was a bit of a nightmare during the afternoon. To handle the afternoon crabbiness, we read to her for about 30 minutes and let her have alone time for another 30 mintues. This seemed to help.
All of our girls sleep with air purifiers that produce a good amount of white noise and shutters that block out the light (for the most part). I recommend white noise and darkness! When our now 2 year old (youngest) daughter gets up at 6am, we give her some milk and rub her back (without talking at all) and she usually goes back to sleep for at least an hour.
If your girl is past this and is just really a morning person, think of the future, she will be very productive in the mornings! :) I agree with what other people have said, putting an early riser in front of the TV is not a bad idea. If it is only for 30 - 45 min, you can't feel guilty. Any longer and you might start to feel a bit of guilt. Maybe you will need to adjust your bedtime schedule so you can get enough sleep until she grows out of this.
As with everything in childhood development, kids go through stages. When they are teens, we will be having the opposite problem! We will be posting about how our kids sleep all day and don't get up until noon! Hang in there!!