No specific anti Semitic laws have been made. I do not believe there is anything in our constitution which continues to remains unchanged as it requires a referendum to do so. The Constitution does not confer rights to the citizens of Australia, rather is confers particular powers of each State and Territory upon the Commonwealth of Australia. Some individual rights may be inferred but no specific rights are named.
One may find the UN laws to be useful. As Australia has ratified the UN law relating to racial discrimination, we are obliged to enforce the law with binding Australian legislation. This is done by way of the Racial Discrimination Act (above).
The act has drawn some attention lately, particularly in relation to the balancing ones right to freedom of speech and ones right to live free of discrimination.
I am a paralegal and a student studying a Bachelor of Laws so I cannot provide advice but I can direct you toward legal information, and provide non-specific information. I recommend you seek advice from a lawyer. Especially as it can be difficult to interpret the contentious sections of the Act. One must not make public accusations that condemn another's behaviours unless they are certain that the condemnation will not find them called to defend their actions under the laws of defamation.
Because he was convicted of a racism offence, not an offence of anti-semitism.
He would have faced a similar proceeding regardless of his target.
It just happened that that one was anti-semitic.
Had it been anti-anyone else, he would have faced a similar proceeding.
It's not (or in that case, wasn't) A special law about anti-semitism.