Ithink this is the best website I've found:
http://www.quarantinedomestic.gov.au/destination-south-australia.html
http://www.quarantinedomestic.gov.au/destination-northern-territory.html
The links I've given you are for SA and NT, but you can select a state in the top left hand side. You have to go through the Vic/NSW/SA fruit fly zone and they are very thorough at the check point at Renmark.
Right at the bottom of the page there's some info about another restricted zone within the state.
Looking at the SA page you can't take potatoes in from any other state.
The PCI permit they refer to would be for commercial transport, not tourists.
I usually avoid carrying anything fresh and carry some instant potato, or tins of tiny taters, tinned and dried vegetables when we're going interstate rather than worrying about fresh stuff and quarantine laws.
But you can try some of these web sites for info too:
http://www.cmca.net.au/pages/motorhoming_information/environmental_issues/fruit_fly_zone/index.php
www.pir.sa.gov.au/fruitfly
www.dpi.nsw.gov.au/agriculture/pests-weeds/pest-and-weeds-management/insect-pests/qff
http://biodiscovery.imb.uq.edu.au/Portals/52/oztravelguide.pdf