Quad Bike mounted to ladder?

And if it comes off resulting in property damage or injury will your insurance cover it?

Ladders are not designed for dynamic weight bouncing and vibrating down the road. In addition you have a 4' high bike that will increase torque applied to the ladder.

Leave the bike at home.

The 300lb rating for the ladder is most likely a 'static' rating - ie a big fat guy can climb the ladder with the camper parked. Although I would be doubtful that the manufacturer did any sort of calculations and just had Bubba go climb it to test it. What you are suggesting would be a dynamic load - a load that is there while the camper is in motion. With it hanging way off the back, if you hit a dip or speed bump a little too fast, the effective load could easily exceed 300lbs due to the g-forces and leave your ladder and bike lying in the road.

I wouldn't do it.

I would think about a front hitch and no use the ladder.

A while back a contributor here wrote, "never use the ladder for anything other than climbing to the roof". I've used that as gospel since then.

I probably wouldn't do it without calling Arctic Fox and asking their opinion. If I were going to try it, I would make sure it is strapped so there will be no movement/bouncing around. And better would be if you could get a hitch type of carrier attached to the frame under it to support most of the weight.