The flight crew reported that a large yaw occurred during a night take-off associated with a bump. The co-pilot thought it may have been due to a rabbit, seen running towards the aircraft shortly beforehand. The aircraft left the paved runway surface and travelled for some distance on the grass before the commander was able to steer back onto the runway. Examination of flight recorder data and ground witness marks indicated that there had been no significant deviation in yaw. The investigation concluded that the flight crew had inadvertently commenced take-off whilst aligned with the runway edge.