DD1 was 15mths when DD2 was born but we kept her in the cot while DD2 was in the bassinette and until we moved house.
We put down her matress at the new house and spent some w/ends here with her sleeping in her bed (mattress on the floor).
She loved it, she only got up out of her bed maybe twice (incl day sleeps) and when we moved she was more than happy to sleep in her big girl bed with her pretty sheets, a couple of months later we put her in an actual bed, she has never needed side rails as she was already aware of the mattress boundaries.

Each child is different, some kids love the space and being able to move around without banging on wooden edges etc, others find the never ending amount of space a little daunting.

try the mattress on the floor first if you can, maybe even with her cot mattress, then the single bed mattress then the bed IYKWIM... GL with it all