My DD was 2.5 when she went into a bed. She slept for about a month before that with the side off her cot so it was like a bed. Worked well for transition as we put her doona in the cot with her.

Once she was in the bed, she only ever fell out twice (never woke up either time!) We had a mattress on the floor for the first time as it was fairly soon after the move, but the second she went straight onto the carpet! Didn't bother her though.