Generally, self-employed people cannot collect unemployment. Unemployment is available to those employees who are fired from their jobs. Seasonal work is akin to project work -- you were only needed for a particular period of time...so technically, you weren't fired. Your assignment merely came to an end.

However, there may be some room to play if the carnival pays you as a W-2 employee, or if you are an employee (as well as owner) of the corporation that books the concession stand. Speak to your accountant to determine your options.