A compass is built for a specific band in the hemisphere. Fortunately all of Europe and North-America is in the same band, but the South isn’t so easy. Here’s an image I received from MOSCOMPASS:
According to this, a compass made for Brazil will not work in Australia. It is best to purchase a compass in the region you will be using it in, to insure you’ve got the correct one. Otherwise make sure you order with the country name, not just “Southern Hemisphere”.
Good luck, and Happy Travels!