On Cook's second expedition, he almost saw the Antarctic coastline. Let's assume that he either sees the coastline or at least sees boulders in the icebergs, indicating that there's a large amount of land. Now the geographers (eg Flinders) name that land "Australia". And nothing gets named Anti-Arctica, because that's just stupid.
So what does OTL Australia get named? Would the British stick with New Holland? They were ok with New Zealand. The Tropic of Capricorn goes through it, so maybe a derivation on that (or maybe I've just seen too many episodes of BSG). Or maybe they'd pick some terrible "New" name.