I'm confused by this. Why don't you want her to move in the cot? Is she able to fall/climb out?

I personally NEVER fall asleep within less than half an hour of getting into bed, and i don't really expect DD to either. Bedtime or naptime in my house means DD has to go into her room (she's not in a cot anymore). I put her to bed but i don't go in again and again to redo it unless she is crying or comes out, then i comfort her/put her back into bed with minimum conversation about it. She often plays quietly or looks at her books at bedtime for a bit and i'm totally fine with that. Right now as i type this she's been put down for her nap and i can hear her rolling about in bed. Her sleep is HER business - i decide when she goes to bed, but SHE decides when to sleep.

Learning to fall asleep is different for everyone. There are people whose eyes close when their head hits the pillow and people who need to read, toss and turn, think, before sleep can find them. Unless it's a safety issue or she's screaming her head off the whole time i really wouldn't worry about it. I'd put her down to sleep and listen for her not moving anymore, then once she's asleep pop in and make sure she's warm enough and not in a weird position.

It might be better, if she's the sort of person who CANNOT fall asleep quickly most times, to spend your energy teaching her to go to bed peacefully, rather than struggling to make her lie still and sleep when she can't.