According to the link above:
The 'X' series passport issued in 1917 is one of the earliest passports. It was during World War I that monitoring and identifying those crossing international borders became critical to the security of Australia and its allies;[2]
The War Precautions Act 1914–1915 required that all persons over 16 years of age, on leaving the Commonwealth, possess a passport
I think as Australia was part of the Commonwealth, and Australians were British Subjects (citizens?) that the above may not have applied to those from Great Britain and Ireland.
I'm sure that someone will have a definite answer for you.
Do you have your families arrival in Australia as I would think there should be an indication as to whether there is additional information/other files including passports.