When my oldest turned 2, I moved him into a toddler bed. He had been climbing out of his crib for a few weeks before. He screamed the whole night the first night no matter what I did, even if I was in the room with him. He ended up sleeping on the floor that night, refusing to sleep in his cool car bed. After the first night, I had no problems at all.
When my youngest son got his toddler bed, he was two months short of his 2nd birthday. He was a 26 week preemie and turned 2 in February. He transitioned into a toddler bed very well and he went from sleeping with me for some months because I had recently moved and had not brought his crib.
I would advise using a gate in the doorway every time, even if you live on one level. My oldest used to get up in the middle of the night, without waking me, and go watch T.V. or get food out of the cabinets.
Good luck!