This is the closest thing I have found to a website on this topic trying to use “virtual spaces”. The section here is the only section which notes Sephardic communities in Australia, the wonderful thing about this project is that I’m learning so much myself- gotta love being a student!
One thing to note about this site is that it is clearly written by an American and probably aimed at American viewers.
The Virtual Jewish History Tour: Australia
The long dormant Sephardic community was also revitalized in the post-war period. Since the original community’s demise in the late 1800s, Sephardim had a difficult time gaining entry to Australia due to the racist White Australia Policy instituted by the government. In 1956, following the Suez crisis in Egypt, the government began to allowed select Egyptian Jews to enter the country. In ensuing years, pressure from the Jewish communities caused the government to drop its anti-Sephardic stance. By 1969, when the Iraqi government began to target the Jews for persecution, Australia allowed any refugee who could come to Australia to do so.