What explorer founded Australia?

No explorer named Australia in 1813. Matthew Flinders was the one who first proposed the name "Terra Australis" in 1803 some time after he circumnavigated the continent, and this became "Australia", the name adopted in 1824.

The name "Australia" was first proposed by Matthew Flinders in the early 1800s, as part of the full name Terra Australis,meaning Southern land. The name was suggested in Flinders's "A Voyage to Terra Australis", which was published on 18 July 1814, ironically just one day before Flinders died.

The actual name "Australia" was then adopted in 1824.