On a hunch I checked south australia and would you believe he was actually born there and not in victoria Well at least his birth is registered in SA as follows
Digger - South Australian Births Registrations 1907 to 1928
Surname: BOOTH Given Names: Jack Stuart Date: 1918-02-12 Sex: M Father: Joshua Alfred BOOTH Mother: Mary Jane ADAM Birth Place/Residence: Pinnaroo District Code: Wel Symbol: Book: 13A Page: 494 Cross Reference:
same parents as the marriage in victoria in 1917 and birth of his sister Maybe the family moved around a bit??