Discrimination due to criminal record

Is it unlawful to discriminate against an employee or prospective employee due to a criminal record?
There is nothing in the Fair Work Act which prohibits employers discriminating against employees or prospective employees due to criminal convictions; and indeed the presence of a criminal record will often disentitle an employee to a job; for example teaching children, or aviation. The general protections provisions of the Act also have nothing to say about this and it is not included in the expressly prohibited discriminations such as age, race, disability etc.
There is no statutory prohibition against this discrimination in Western Australian law either.
The Australian Human Rights Commission Act and the Human Rights and Equal Opportunity Act collectively set up a regime in which the HEROC Commission can attempt to conciliate claims based upon discrimination in the workplace because of criminal convictions, but it is a toothless tiger because it cannot arbitrate or award compensation or any other form of meaningful relief.