Blues Brother, in answer to your questions:
Providing that their understanding is correct and the Governor General confirms it...
The GG will approve it. Essentially, under the Constitution, the GG approves whatever the Prime Minister tells the GG to approve. (There are exceptions in extreme circumstances, such as “the Dismissal” in 1975.)
[Edit.. why does the Queen's representative have to get involved? It ought to be down to the Aus. Government ]
There is a legal fiction that Australia is still ruled by Queen (or King) of England. Under the Constitution, the Queen appoints (or fires) the GG. In practice, the Aust Prime Minister appoints the GG, but the GG is often referred to as the “Queen’s representative.” The GG exercises the same powers in Aust, that the Queen exercises in UK. Just as the Queen stamps whatever law the UK Parliament sends to her, the GG stamps whatever law the Aust Parliament sends to him/her.
In other words, loss of charity status is a “done deal”. Just a formality from here.