I tightened up the steering a good bit on my daughter's Dora Lil Quad by running a bolt that is 1/4 inch in diameter and 2 1/2 inches in length through the plastic steering column. I used a nut and washer to secure it in place.
In addition, I ran a bolt through the part shown below to prevent it from coming apart when my kids lift up the front end. It didn't come apart extremely easy before, but it was still possible.
"We may one day have both fame and fortune, and learn that neither is basic for true success and complete happiness." ~The New Era, August 1989, pages 4-5.