Ric Flair makes a good point. While my hauler only has a 10 foot garage, it would haul the load you ask about just fine. When you shop for your new rig be sure to look for cabinets and such that could get in the way. I have a large overhead storage on the left side but a golf cart would go under it, even with a top on it. There is a lower cabinet on the right front end but it would not interfere with this load either. If it did, I could reverse the load with motorcycle on right and quad (or cart) on left because the bike would not go far enough forward to hit this cabinet.
Toy hauler manufacturers pretty much know what we haul and design the garage for the purpose. When people want to haul unusual loads (JEEPS, Smart Cars, dune buggys etc.) is where the problems enter.