The mom who suggested the gradual approach, gradual transitions has the right idea.
At this point, 2 and 1/2, your daughter has formed a strong sleep pattern, falling asleep with you. It is only natural that it causes her extreme anxiety to do something so different as to be left alone. Although she may look like a "big girl" compared to the baby she was, she's still a "baby" in many ways. And is not ready to comprehend what's going on and simply accept an adult's explanation.
Your best bet is to start with something close to what she is used to, and very gradually change her over to a new way of doing things. You could try what the other mom suggested with the toddler bed. And/or you could have her fall asleep in your bed, but with you sitting next to her instead of laying down. Then moving to a comforable chair. Eventually you'll be able to leave when she's almost asleep. Then to leave a little sooner, etc.
What you want is for her to develop a sense of trust and security that even though things are a little different, its still okay.
Be prepared for these to take a while. A few weeks at least.
As for the crying it out suggestion, I fear you would be in for a long seige. She's not an infant -- she has the will and long memory of a 2 and 1/2 year old! At this point, this approach would only work easily with a very passive tempered child.
If she was a child that just couldn't fall asleep, up at all hours, very irregular sleep patterns, then maybe it would be worth the battle of going that route. And would then also be in the child's best interests as well.
Also, in regard to moving the bed time up earlier -- pick just one battle at a time. Decide which is most important to you now, getting her to fall asleep without you laying there... or to get her to fall asleep earlier.
Be aware that if you get her to sleep earlier, you may have her up earlier as well.