My son went through the same phase around that age, and we actually kept the mattress on the floor for a good few months because it was the safest option while he was still getting used to sleeping alone. When he was a bit more steady, we got a simple low toddler bed frame from Courts so the height was not too scary if he rolled off lah. I would hold off on a bunk bed until he is at least four or five, just because the climbing up and down can be risky for a two year old.