Unfortunately you have just missed out on the
Working Holiday program to teach English in Japan.
However, not all is lost. If you have a Diploma, it's still possible to get a work visa to teach in Japan. However, it would be very difficult to gain work if you are in Australia. There would need to be some risk on your part to actually fly to Japan and actively seek work.
I have seen casual job ads in Japan which may help you as a stepping stone to finding your teaching job. Such jobs as bouncers for a night club, handing out flyers for English schools etc. The pay may not be the best (approx. ￥1000~￥2000 per hour), it can take the pressure off and meet your living expenses.
Taiwan and Korea are like Japan. They both require a tertiary degree to find work and be granted a visa.
China is much easier and definitely worth pursuing based on your background. Although the pay is much lower in China, so too are the living expenses. You may even consider 1 month volunteer work in China as an option.
Hope the above helps.
Cheers!