Sydney is generally a pet-friendly city, but it does have breed-specific legislation in place. The following breeds are not permitted to be owned in the state of New South Wales: American pitbull or pitbull terriers, Japanese Tosas, Dogo Argentino, Fila Brasileiro. If you already own one of these dogs you must have it spayed or neutered and registered with the city. As an expat, you will not be able to import these breeds.
Helpful Pet Resources
Pet Restrictions: What to know before you relocate your pet overseas.
?What you need to know on relocating your pet abroad.