Yeah Quickeze towing are awesome, $55 weekdays from memory, as Aurora said, theyve towed my car around quite a bit
But no theres nothing wrong with your dad towing you, just make sure you keep lots of distance from him, keep the key in the ignition turned to on so the steering doesnt lock, and dont crash into him. If your dad is a more "seasoned" driver than yourself, id reccomend him being in the skyline and you driving his car, as it takes alot of skill/confidence/prediction so you dont crash it into the back of his car