Go karts are one thing. Off road go carts another. Many years ago, my father helped me make one (with great concern for my safety, he did 90% of the work). We salvaged a metal fire-engine cart (old christmas present) for the front end stearing, and used wood (chassis) and the rear wheels were ment for wheel barrows. It was mostly cobbled together. I grew out of it before the plans to retire his Briggs & Stratton (~2hp) to my gokart were realized.
I think for a basic off roader, you would want to first have a strong chassis and other componets lending themselves to abuse. Depending on your resources, you may want to get parts from atv (as suggested by other users). You will likely need a stronger engine...and then start to install the many safety devices to help junior return relatively unscathed from his adventures (ideally).