After having lived through the lockdown in Melbourne myself, I think it's pretty unfair to the people here to suggest that the reason the cases are so low is because it's just "a big empty island", and not the result of the fairly hard lockdown that the people here had to endure.
The GP didn't say it was because Australia is geographically large, it said it was because Australia is geographically isolated and population-wise comparatively “tiny”.
what does a country's population size have to do with it? if you mean density is a factor, that's surely only true at a local scale (cities with lots of people mixing every day, crowding into subways, elevators, and cramped factories), and not averaged over a vast area such as a country? Australia has cities as dense and populated as US cities, and with a few exceptions (eg SF) the American ones suffered much worse outbreaks.