Firstly, Australia is not a republic, rather, it is a Constitutional Monarchy and has been so since Federation on 1 January 1901.
That said, Amber should take a look at Australia's Table of Precedence of 5 October 1982 (see below)
The Prime Minister is third on the list; that would make the wife of the Prime Minister the 3rd Lady and not the First Lady would it not!
And here's another point. What if Australia were to be a republic what then? Surely the wife of a President of an Australian republic would be the First Lady and not the wife of a Prime Minister.
Two more people from the media now assert that the wife of the Australian Prime Minister is "the first lady". They are 2GB's Luke Grant and Nine News UK Correspondent Amelia Adams. The following is a small burst from a discussion they had about the recent G7 summit in Biarritz, France.
When will the media learn?
Further information about the Table of Precedence is available here.