Carbon fibre is no good for combat. It is very strong and stiff but not very tough and would snap and shatter very quickly. There would also be no quick way to fit it at an event.

Glass fibre, with some careful design, may be more suitable as it is not a brittle but most people don't use it as if it gets damaged then your chassis is a write off for that event. It has been used for armour in the past but for a chassis I can see it being more trouble than its worth.