If the compass is moved to Antarctica, would it still work? Discuss.

To answer this question you must remember there is a difference between the magnetic south pole (where the S on a compass points) and the south pole based on the axis of rotation of the Earth. Normally, when you are using a compass, your distance from both points is high, and so the error between magnetic south and geographic south is small. In North America, you might be able to have a good estimate of "South" based purely on the compass.
Once you get to Antarctica, though, the difference between the actual South Pole and the magnetic south pole is much more obvious. The geographic south pole is about 1300 km from the magnetic south pole, which is close to the Vostok research station. Unless both of these points were in line with your compass, there would be a big difference between where your compass says South is and where geographic south truly is. 
A good way to illustrate this idea is looking at what happens if you were to take a trip away from the true South Pole towards Vostok station. By definition, any direction away from the South Pole would constitute "North." However, as you walk to Vostok station, your compass would say you are going south! Similarly, if you were to turn around (because walking 1300 km is more than most of us would consider doing in Antarctica), your compass would say you are going north! If you were to deviate from your path significantly, your compass would have a similar large error.
The important aspect of this question is the location where you might wonder whether a compass would work. When two points are close together and you are far away, you might be able to consider them close enough to the same point. The closer to them you get, though, the more important it is to consider them separately.
http://www.aari.aq/stations/vostok/vostok_en.html