The following link will provide you with a filtered list of only those (60) schools in Sydney that are able to accept internationals students. We cannot provide any information on whether any of those schools have short term vacancy for the first term of 2014. You will need to select your preferred schools and contact them individually.
However, rather than simply contacting every school we would recommend using the map at the bottom of that page to locate schools that are near to where you will be staying while in Sydney. The map is not filtered (which means it displays around 500 Sydney schools). But any schools that are nearby on the map AND also appear on the list above are where you should start your search.