It depends on your local council as they all differ from various States and Towns. If you want to keep more than two dogs, with a maximum of four dogs per residence, you will need to apply for a permit.  To look up what your local says about pets, navigate to the Australian Government website and click on the State you live in and then click on 'Local government directory' and type in the name of your suburb. The Council responsible for your Suburb should appear, and you can investigate their website as to what they say about looking after the number of Pets.