YES
You can drive your Primary Producer Registered vehicle to the football. 

As long as you are not carrying on another business for reward (money or goods), you can drive anywhere.

South Australia
Motor Vehicles Act 1959
Version: 1.7.2016

34—Registration fees for primary producers' commercial vehicles
(1) If the owner of a commercial motor vehicle—
(a) satisfies the Registrar by such evidence as the Registrar requires that the owner is a primary producer in this State; and

(b) undertakes that that motor vehicle will not, unless the balance of the prescribed registration fee is paid, be used on roads for carrying Her Majesty's mails, goods or passengers for pecuniary reward or for carrying goods in the course of any trade or business other than that of a primary producer, the prescribed registration fee for that motor vehicle must be reduced by the prescribed amount.

(2) In this section—
carry, carrying and carriage respectively include haul, hauling and haulage