The only space for a cot in our room is at the end of our bed. How do we keep our bedding (doona) from being pulled into the cot by our baby?

I think it would be very difficult for a baby of 4.5months to pull adult bedding into a cot in a great enough amount to cover baby’s head &/or face.

Is your daughter rolling yet?
If so, she needs to be moved to her cot & cease swaddling/wrapping (she needs her arms free).
It’s essential to stop wrapping as soon as baby starts showing signs that they can begin to roll, usually between 4-6 months. If you wrap baby, consider baby’s stage of development. Leave arms free once the startle reflex disappears around 3 months.
If you are using a bassinette, it is time to transfer baby into a cot as soon as they first show signs of being able to roll.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over