She also has always been an awful sleeper and needs very little sleep. I sed to not be able to get her down till midnight everynight....once she dropped her nap 5 months ago she now goes to bed at 9:30, but this means she is up from 7:30am-9:30pm going non stop, no break, and it is still hard for her to stay still enough and stop fidgiting to go to sleep.
Mine dropped naps at about 27 months and gets up between 6:30 and 6:45am no matter what time she goes to bed! Normally we put her to bed at 8:30pm but sometimes she'll want to work in her workbooks until 9pm-ish.
She doesn't sit still...hardly either and goes all day long! Add a one year old who is just as active into the mix (she does take two short naps during the day) and I am one tired mama!
So you are not alone!
ETA: I do put her in front of the TV to "settle down" and she does when I need her to. She likes Wow Wow Wubbzy and that seems to work! LOL