The Key On vs Off question is determined by the type of steering column the Camry has (locking or not) and whether the dolly brand requires steering to be locked or unlocked. We can't answer the key question without knowing more about the specific dolly brand/type or the year of the Camry.
In some situations, the dolly requires that the steering be locked and the car doesn't have a locking steer column. My Master Tow dolly coupled with my Buick Verano is like that. I use the seat belt to strap down the steering wheel when I tow, so that the front wheels can't turn.
Former owner of 2004 American Tradition
Home is in the Ocala Nat'l Forest near Ocala, FL