By 12,000 BC early people were living on every Continent but one, what one was that?

Antartica is most likely the answer.

The date is questionable, based on prehistoric evolutionary assumptions, and there is no written record of anything existing that far back.

However, Antarctica is the obvious answer for any time in the last several thousand years.

" The possession of fire and tools with which to make clothing and shelters made it possible for different human species to extend the range of their habitation far beyond the East African savanna (grassy plain) zone where they had originated. During the last Ice Age, which began about 2.5 million years ago and ended around 8000 B.C., humans first moved northward from Africa into Europe and eastward across the present-day Middle East into central Asia, India, and East Asia. Neanderthals and related peoples were found across this
zone as late as 35,000 B.C., and some archeologists claim that by then they may also have begun to migrate across a land bridge into the New World. By 10,000 B.C., groups of the Homo sapiens sapiens species had colonized all of the continents except Antarctica. Glaciation, which had caused a significant drop in sea levels, resulted in land bridges to the New World and Australia.

By the late Paleolithic period, around 12,000 B.C., human colonies were found in North and South America and in the south and west of Australia. Thus, long
before the rise of civilizations, human societies had proven themselves capable of surviving in widely varying climates and terrains."
Source and further information:
http://history-world.org/paleolithic2.htm

So it would be Antartica...

Antarctica

Everyone seems to think it's Antarctica. Why? Has Antarctica been frozen for the entire duration of Earths LONG history? Why have fossils of temperate, and sometimes even sub-tropical, flora been found on the continent of Antarctica? Scientists have discovered fossilized trees that would never have been able to survive in a climate that has six months of darkness. The question itself sounds bogus, and my answer is there is mounting evidence that the earths poles(or at least the land over them) shifts over time, over ages. Dont be so sure it's Antarctica...

"The Kingdom of Zeal floats above the planet, avoiding the ice age raging on the surface below. Geographically, it consists of one major and three minor continents. A system of teleportation devices called "skyways" facilitates transportation between the floating continents and also with the planet surface. There are three major cities: Zeal Palace (the capital city), Enhasa, and Kajar. Queen Zeal rules the kingdom as an absolute monarch."
Source and further information:
http://en.wikipedia.org/wiki/Chrono_Trigger_time_periods
Unfortunately, I did not found which of the continents had no inhabitants...

Antartica I would guess

Antartica

As the geographic north pole was then in southern Greenland, parts of Antarctica would have been habitable. Whether they were or not is at the moment pure speculation since the land is still under a mile of ice.

Australia would be the next best guess, but I seem to recall reading that the Aborigines arrived 8000 years before that.

New Zealand. :)

G'day Highlander,

Thank you for your question.

Antarctica which has only had short-term human inhabitants since the 20th century.

Regards

The Sea