We have a single duvet and tuck it in at the foot end of the bed. I didn't want to have to buy a toddler bed duvet and then another single one when DS1 moved out of his toddler bed IYSWIM. We do have a summer weight one and an autumn/ winter one.
Because the size of the cot bed is smaller it automatically retains more heat when the child is sleeping, however, the larger surface area in a single bed means the child only heats the area he/she is sleeping in, therefore, a higher tog rating is required on the single bed size. The single bed size comprises of 2 x 4 tog duvets that popper together giving flexibility to reduce the tog to 4 togs when the nighttime temperatures increase.
Do not exceed the maximum recommended tog duvet, which is 4 tog for children in cots or cot beds and 10 tog for children in single beds
We're about to do same with dd - i have bought a 4 tog single duvet from ikea and have put it across the bed (also cot bed) sideways iyswim and tucked excess down side. I didn't want anything too heavy or hot at this age. On cold nights she can always have an extra blanket. Good luck