My DD started doing that at 16months and it took me a week to figure out she was done being in the cot.
We got her a bed and all was good. She's never had a rail but she sleeps like a log and has only fallen out at night once. I did originally used to put pillows on the floor next to her bed and we went straight to an ensemble (cos at 16months even she was nearly too long for the cot - she's pretty tall) and so we just took the feet off it so that it sat on the floor.
DS on the other hand has never ever slept in a cot and only in a bed with a bedrail....