Alex its always good to question what your told, regardless of who told you.
To answer your question there is environmental monitoring going on all the time in Australia. The Syncrotron in Melb constantly monitor air quality, as do other nuclear science bodies in the country (ANSTO, ARPANSA). Indeed, you have nothing to fear.
The other part of this is that the bodies of air between the northern and southern hemispheres do not mix. They approach the equator and swirl back around. As such, studies of soil samples in the southern hemisphere show radionuclides from atomic weapons testing by the British and French governments in the pacific region in the 50's. Soil samples in the northern hemisphere also show evidence of weapons testing around this time in the northern hemisphere but also of the Chernobyl accident in '86.
So two part answer:
1. Yes there is plenty of monitoring in Aust
2. Radiation from Japan will not travel to Aust
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