A friend of mine did exactly this a few years ago. He used a Formula Ford race car with a custom made one seat fiberglass body on it.
The body should be insulated from the chassis (rubber mounts are best) or else the vibration may crack the fiberglass over time. Take a loot at a typical pick-up truck. Look underneath. You will see the body is bolted to the frame. The bolts go through these rubber biscuits, so the body actually sits on rubber. This rubber allows the frame to shake and vibrate a bit without harming the fiberglass.
You may be able to engineer a similar arrangement for your project.