Ive done what you're planning, a few times. Building one now with a 250cc quad motor. I dont know how far you want to go with the conversion or what your skills are. Here is a simple approach. ...
Whack off the existing steering on kart. Cut up quad just BEHIND where it all ties together. (Keeping everything intact) Now you gotta figure out how to mount that assembly to your kart , reinforcing everything along the way. HOPEFULLY the wheel track is wide enough to suit the rear of the kart as well. Now you got front suspension. ....
Next, if you dont want to get REAL involved in a conversion, the big fat balloon tires add some bounce and absorbs some of the bumps. Just get a 1" solid live axle and some QUALITY pillow block bearings ,some locking collars, and some hubs that will fit the wheels you got. A sprocket,sprocket hub,a some brakes. I prefer hydraulic disc brakes, but band brakes work pretty darn good too.
Now, all ya need is a bike/quad motor about 80-200cc will work. For simplicity, find one that is semi-automatic (no clutch lever) If you have to use a manual,no big deal. I can walk you through that too. Its not rocket science, its more fun than that..... lol