I know how it is. My 7-year-old is still this way (minus the whining and crying, thankfully). Some kids just don't need much sleep, and he is one of them. He's at an age now where he will usually just lie quietly and daydream or hum to himself until he drifts off, but it was rough when he was younger.
However, I agree with both Dawn and Victoria that other things might be adding to the problem. Out of curiosity, what is your rationale behind not bringing her into your room until she's asleep? If it's that you want some adult time, could you just bring a book for yourself and snuggle with her for a while until she gets sleepy? Is it possible that, since she knows she'll end up in your bed, she's staying up in hopes that she will get the comfort of having you next to her as she drifts off?
Increasing physical activity in the afternoon has helped us some. If the weather doesn't cooperate, your daughter could jump rope or do tumbling exercises in a den or playroom, or you could challenge her to see how many jumping jacks she can do, etc.