Write a very polite and short letter simply asking permission to have a cat (not mentioning all the other factors) to the Executive Committee of the Owners Corporation, either directly or via the Strata Manager if there is one.
Check out the Strata Titles Act NSW where it says the Owners Corporation are not allowed to unreasonably withhold permission for you have a pet.
If they say no in writing, then it might possibly be time to seek mediation via the NSW Office of Fair Trading and mention that the cat has actually been living with you there for several years without causing any problems etc. 'Keep your powder dry' until it can do you some good, i.e. in a forum such as mediation.
As Jimmy T has often said, pets are good for people to have for a variety of reasons.