You should enquire with your Strata Manager if there are any By-Laws in place regarding pets at your building, as some buildings have very specific rules in place and some buildings allow for no pets whatsoever.
Should your building operate under By Law 16 of the Strata Schemes Management Act 1996 (refer Support > Document Bank for By-Laws) you should fill in the Pet Application Form and forward it to your Strata Manager who will notify the Executive Committee of your request and their subsequent decision.