Hi K.,
I had the same problem with my son, however we recently managed to improve his sleeping habits. My son is 23 months old, and he is just now starting to get enough sleep (in my opinion).
Our first issue was sleeping through the night, which he finally started to do at about 19-1/2 months. He had to "cry it out" for several nights until this worked.
Second issue was getting him to go to bed at night. We do bath, a little play with dim lights, read two books (reading by 8:45 pm) and then it's in the crib wether he is asleep or not. Yes, he's still in the crib. This way I don't have to worry about him getting out of bed. I thought we'd train him to sleep while in the crib, and then switch to a toddler bed. (Not sure how this will all go once he's in a toddler bed, though.)
I am temporarily home on maternity leave with my second son, but when I was working my hubby and I were up and out of the house by 6:15 like you, and we had family come over to watch my son so he didn't have to be up so early. Although he did not need to wake up that early, he usually woke up before we left for work. Now that I'm home, he sleeps in a little longer. Your daughter might be getting up early to see you before work (that's what I think mine was doing). So you might need to get her to bed as early as you think necessary because you may not be able to get her to sleep in any longer int he mornings.
Then naps...I read my son two books and then it's in the crib for "happy nappy" time, which is atleast an hour. If he cries, I just let him cry. I leave him with a book to "read" incase he doesn't want to sleep, but he stays in there for one entire hour. If he falls asleep, then I just get him once he wakes up. He usually falls asleep after a few minutes of fussing or talking to himself, and then sleeps for 2+ hours. Before I started this routine, he was taking 45-60 minute naps, if he napped at all.
I used to think that my son was just wired to not sleep much, but then I started reading that kids will fight sleep more the more tired they are, so they may seem like they are full of energy when they are actually exhauseted...Your daughter is probably ready to go to sleep earlier, but she just doesn't want to miss out on the fun, and maybe she doesn't know how to calm herself down to go to sleep.
This is just what works for us. I hope you find this a little helpful and I hope your daughter starts sleeping a little more - for both her sake and yours! :)
K.