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Ask for a copy of the by-laws and see what it says in relation to keeping animals. Have a look at the Adjudicators decisions on the Qld Dept Justice and Attorney General's website http://www.justice.qld.gov.au/3269.htm where there is a decision directly related to the keeping of pets. The Act does not discriminate between owners and tenants and neither should the by-laws. I am not a lawyer just a tenant who reads a lot and has a difficult body corporate.
most body corporates in NSW do not allow pets, a combined decision made by the owners at the time. but it can be changed provided the owners agree. although if the Landlord does not agree to having pets in the unit even if the body corporate allows it you would still have to get rid of the cat. you could try to fight it and get written letters from neghbours stating that they have pets and approval from strata. if this is the case and you landlord agrees to having a pet you could potentially have a good chance at your local tribunal.