Sorru tropico. no go
Unfortunately you won't be able to work in Oz if you don't have residency or a working visa. I'm not aware of any school that has foreign instructors. You can apply for a holiday working visa which lasts a year but you cant work for any one employer for more than 12 weeks. Sponshorship is a road that employers can go down only after proving to dept of immigration that they cant find a suitable qualified person in Australia to fill the position they have vacant. We do have shortage of instructors but not a severe shortage just yet. Most schools have plenty of Grade 3 instructors but lack a little in ME and IFR position. Sorry to rain on your parade.