I knew there was something dodgy about all this. Section 105A says owners corporations can’t charge fees for considering pet applications. The OP should ask for her money back, citing the the Strata Schemes Management Act, Section105A (below). There is no need for a new by-law to allow pet fostering, but the committee might refuse to allow an excessive number of cats if they can show they would prove a nuisance. And, by the way, there are other parts of the legislation that cover animals that have been approved but later prove to be a nuisance.
105A Bonds or fees relating to keeping of animals not payable
An owners corporation must not require an owner or occupier of a lot to—
(a) pay a bond or fee relating to the keeping of an animal on the lot, or
(b) obtain insurance for an animal kept on the lot.