I know the ocean is big, and exploration far away from home is difficult, but Antarctica isn't exactly easy to miss either. Did no one in the late 17th or early 18th century, well after Australia was colonized by Europeans, decide to just sail south and see what happens?
And furthermore why, all of a sudden, in 1820, a whole 3 different nations made near-simultaneous claims of discovering Antactica - Bellingshausen (Russia), Bransfield (UK), and Palmer (USA)? Is this a coincidence or a planned "Scramble for Antarctica"?
It's actually very easy to miss.
It's not on any trade route, the oceans surrounding it are incredibly rough (discouraging wayward ships), and as you get close there is sea ice and bergs (bad news in a wooden boat).
Figure that the motivations for exploration were largely financial. Until the early 1800's there wasn't anything to gain by exploring southward. As whaling and sealing became major industries, the Southern Ocean became worth the risk.