What is the only country in the world that is also a continent?

Australia.

Geographically, the country of Australia is a continent, not an island. As a landform, it could be considered an island as it is entirely surrounded by water and not joined onto any other land mass. For this reason, it is often referred to as an island continent. Australia is too big to be formallyclassified as an island. The world's largest island is Greenland.

Australia can also be taken to be both a continent and a country, if we accept the definition of continent as being one of the large continual land masses on Earth (which would exclude nearby countries such as New Zealand, which are not part of a continuing land mass).

Another reason why Australia is also considered a continent is because it sits on its own tectonic plate.