A.C.
Have you tried to get her to nap longer? Or perhaps two naps?
My daughter, 19 months, goes to bed between 8:30 and 9:30, wakes up between 7:30 and 8.
But then she takes a two-hour nap in the middle of the day.
Also, just because she wakes up at 5:30 doesn't mean she has to get up then. At 20 months, she's old enough to entertain herself for a little while when she wakes up. I have a couple of books in my daughter's crib, and she reads them before going to bed at night and when she wakes up in the morning. Frankly, I had never stopped to calculate how many hours she is getting. I watch for signs of sleepiness and crankiness. If your daughter is seriously sleepy, leave her in bed or even rock her back to sleep at 5:30 in the morning, and then talk to your pediatrician about other methods to help her sleep. Good luck.