Hi K.,
Don't worry that you have screwed up your child, you sound like a great parent.
My older son was like this...he wouldn't go to bed until 11:30--and no daily nap! My husband and I would be passed out from exhaustion on the couches, and he would be running around waking us up. We started putting him on a strict nap/bedtime schedule so we could get some rest. Since he never was a napper, it was hard the first few days--took me an hour of putting him back in bed just to get him to take his first scheduled nap, and boy did he scream--but after about three days he settled down. They say it takes your internal body clock three days to reset itself, so this makes sense. Sometimes now he has a little trouble with nap/bedtime, but for the most part he has adjusted to this schedule.
Now, my eleven-year-old is a different story. She takes forever to get up in the morning, and is frequently late to school, no matter what time she goes to bed in the evening. She must be like her father, who is the same way. I guess some kids (and adults) just function on a different daily schedule. You could try adjusting your daughter's nap/bedtime schedule (and stick to it!), but you never know: she may have trouble with mornings forever. Don't let it get you down, though, because eventually she will be old enough to choose which hours she chooses to work and sleep each day.
Good Luck!
M.