Don't move him until he is ready. My DS never slept in a cot (he screamed in the cot, not the bassinet though...) so was always in a bed (we coslept then he got a queen mattress on the floor.
My DS moves heaps. I found that a toddler bed was way way way too small. My lucky kid got a double bed in his big boy room fo grow into. I find he wakes less with a bigger bed and DH/I can always sleep there if he is sick etc etc.