What continent has the fewest countries?

Antarctica, it has no countries.

Antarctica has zero countries. By agreement, no nations exert their territorial claims over the continent.

Australia is an island continent with one country. Australia's mainland is a continent that is politically composed of a federation of 5 independently sovereign countries Not counting Tasmania, which is an island hugging the south east coast. These have their own constitutions and governments and since federation in 1901 have been referred to as states. There are also 2 territories on the mainland that are administered by the federation on behalf of the states.

(the term Oceania is normally used to mean Australia and other regional countries)

South America has 12 (or 13) countries, the fewest of the continents with more than one.