First of all, try putting her in a play pen to sleep. They are harder to get out of. She's old enough where it won't be a breathing hazard like an infant.
Secondly, make sure she is still napping during the day. It might sound crazy, but she needs to keep napping in order to sleep at night, it has to do with babies' sleep cycles.
Thirdly, you might want to give her a bottle of milk about 30 minutes before bedtime to fill her up. She might just be getting hungry... just be mentally prepared for possible diaper leaks in the morning.
Fourthly, she's old enough to understand you mean business. If she wakes up that early after all you have tried, put her back to bed and tell her she needs to stay there until the sun comes out. This might take a few days for her to understand. My daughter is 23 months and is still getting used to the idea that she has to stay in bed until it's light outside. (It took a month of training and some serious insomnia for me. She sometimes comes out at 6:30am, but its better than 3am or 5 am!)
Hope that helps.