As far as I know, you can't permanently fix it yourself, no... not unless you want to void the warranty and potentially destroy the system.
RRoD'd consoles are under a three year warranty anyway, and seeing as the 360 was released on March 2006 in Australia, the console will still be under RRoD warranty (unless the seller foolishly tried to play handyman and fix it hisself). If it's a US console then there are still a few days left for launch units - the US and Canadian launch was November 22nd 2005... though I don't know if you'd want a US unit. Is it cheaper to import the games and pay import tax (does Australia have that?) than pay an exorbitant amount in the Australian shops?