"I have written to the Governor General asking her to commission Rudd as Prime Minister of Australia."I don't know anything about this situation, but ...
... peaceful replacement of one leader by another is an astonishingly wonderful thing, and one of the great inventions of democracy. Or if not an invention then at least highly polished by democracy.
Just since 1945 in the UK: Churchill, Attlee, Home, Wilson, Heath, Callaghan, Thatcher, Major, Brown. Whatever you think of these people, they all lost an election (Thatcher's a party one like Gillard) and handed over power to somebody else because that's the way democracy works.
There is PLENTY to complain about in democracies and the way politicians work. But sometimes let's pause and celebrate this fact. Let's not forget that engineering a peaceful takeover by his political opponents won F W De Klerk the Nobel Peace Prize.