It depends if you are looking at a temporary or permanent move. If it is permanent then GCSEs are irrelevant as there no 16 year old qualification in Australia. It is expected that the vast majority of children will be at school until they are between 17.5 and 18.5 and they leave with a qualification at the end of that (Year 12, the 13th year at school). If you are looking at a temporary move, or not sure, then you will need to bear in mind the timing for his education.
Also your visa type may impact on your liability for school fees in some states. Many states now charge thousands of dollars per head for temporary residents to use state schools, so make sure you are across this. Where are you thinking of moving to?