An employer has the right to employ anyone he/she chooses as the right fit for his/her company. The TRA or other authorities offer their information requirements as guidelines to follow. If you encounter a worthwile employer and form a quality relationship, they would be more likely to bat for you and not be concerned so much at what the regulation says.
When I owned a business in Melbourne, I would have travellers often call in or phone me looking for work. The ones that came in, if they had experience in the trade were definitely looked upon more favorably than those without.
But, if they had qualifications that werent Australian qualifications, I would not refuse them on those grounds. It depends on the employer.