Thanks for the input.

DD1 will begrudgingly fall asleep in the car without one, so I guess that's a start.
She's always slept extremely well, so I hate the idea of possibly messing with it! On the other hand, she was extremely attached to her sleeping bag and I thought we'd never get her out of that, but when she moved into a big girl bed with Dora everything, she was happy to go without it....
What does she say if you ask her? Is there something she would like to swap the dummy for?