First, I would take her to the pediatrician (if you haven't already) and have a full physical done. At least, then you can make sure that nothing physical is going on.
However, as a veteran mom, my instinct tells me that she simply has too many choices available to her other than sleeping. She can play around, come in your room, have a drink of water, etc. When she was in the crib, her mobility options were limited, but now that she is in a big girl bed, her choices seem limitless (to her). My suggestion would be to keep a short nap in the afternoon (no more than 1.5 hrs), eliminate all possible choices (she doesn't need water in her room, put a gate up so she can't wander into your room, put all toys other than one lovey out of reach), and get on a very strict routine (wake up at same time, bed at same time, dinner at same time, bath at same time, etc). Try it for 3 months. Even if she is a "true" insomniac, these things will still help.
I know it seems like "tough love," but as a mom of 6 kids, I know keeping your kids healthy through sleep (and you, too!) is really important.
Good luck!