NSW Ruling:

NSW there was a case where the High Court of NSW ruled that NSW strata schemes will not be able to include by-laws that ban animals.
While this does not currently affect Western Australian legislation it may be a consideration for SAT disputes. 
The resolution was unanimous with the three court judges viewing the attempt to ban animals from the scheme as a breach of state legislation.

If you would like to read further you can do so by clicking here.

Western Australian Context:

There is no default law restricting pets in strata living, however your strata property may have specific by-law written in relating to pets.  

If so, this will be in the strata documents you received when you purchased your property. If you are a tenant – it will be in your tenancy agreement. It is your responsibility to always check before bringing a pet to the property.

The default by-law relating to the keeping of pets is contained in the Schedule 2 By-laws of the Strata Titles Act 1985 at Schedule 2, by-law 12(c)

12.  Additional duties of proprietors, occupiers, etc.

A proprietor, occupier or other resident shall not —
(c) subject to section 42(15) of the Act, keep any animals on the lot that he owns, occupies or resides in or the common property after notice in that behalf given to him by the council.

The usual interpretation of the by-law is that pets are permitted on strata properties until such a time that they become a nuisance.