Hey, the "me" time you are talking about comes about 2 years after your child graduates from college.
Here is the solution. Sleep when you child sleeps, be awake and very active when she is awake. Read to her, show her how to sweep, how to feed ducks, how to play dolls and house, how to hop on one foot. PLAY. Both of you will be tired and your "me" time will be playing with your child.
If you don't like to play with a child ---don't have them. I would even suggest you give your child to a family who wants a child.--even at 6 a.m.
Toddlers need structure, but they will get up when they get up, and YOU do not need to be getting 9 hours of sleep and me time every day. It is you toddler's time now.
Get up before your child, and have her day planned out. Wear her out everyday and don't let her nap.
Where is the other half of your family that could help you--you know a husband ? NOW you know what they are for.