Common sense would dictate that GP is talking about the country not the continent, as continents typically do not have heads of state :)
While that is true, it's not typically how the phrase "Australia's history" is interpreted.
It's common for "Australia's history" to refer to pre-colonisation in addition to the last couple of hundred years.
This is almost certainly because Australians see the country and the continent as 'the same' for all intents and purposes.
However, I think there is nothing further to be gained here as we would be arguing semantics.