Per Beverly, (in a hypothedical) Australia still existed in the year 2161. She didn't seem to be referring to the continent, by to the country.
Sorry for nitpicking, but the continent is not called Australia. It`s called Oceania.
I think the Star Trek universe has countries, but a ruling body on top of that. Kinda like the US works today with states and the federal government. And more to the point as history shows the likelihood of the same countries existing as they are today, for so long, is unlikely. Especially when you consider all the conflicts that occurred on earth like WW3 and the eugenics wars.
"World War III itself ultimately lasted from 2026 through 2053, and resulted in the death of some 600 million Humans. By that time, many of the planet's major cities and governments had been destroyed." (http://en.memory-alpha.org/wiki/World_War_III