Actually we had an Australia army at that time, and earlier. The Australian Army was established on 1st March 1901.
Take a moment to read what I actually wrote: "There was, I asserted, no such thing as an Australian "army" -- defined as a permanent or semi-permanent organizational unit composed of two or more corps and having a dedicated command structure
-- during World War II.
"Army," unfortunately, is a term susceptible to two meanings: (1) the entire military establishment of a nation's land forces; and (2) the highest-level permanent or semi-permanent field unit in a nation's land forces (a problem, btw, that has no counterpart for maritime forces, where the distinction is between "navies" and "fleets"). Thus we can say that the U.S. Army (sense 1) trains its officers at West Point, and that the U.S. Fifth Army (sense 2) fought in Italy in World War II.
As I have consistently pointed out, there was no Australian army (sense 2) in World War II. There was an Australian army (sense 1), but then it's highly unlikely that Rommel (or anyone else) would say that he wished he had Australia's "military establishment." I will, therefore, charitably ascribe Scaramouche
's error to a common misunderstanding rather than his demonstrated truculence.