You are opening a can of worms here (or a bag of cats) so you are right to be cautious. If you want to maintain your (almost) pet-free status, you could modify your by-laws to say that genuine assistance animals must be restricted to one per unit and must be approved under the terms of the Local Government Act (see this advice fact sheet) and that it must not be allowed to roam on common property on its own.
If you are taking this as an opportunity to modernise your pet laws (or at least discuss the issue) a reasonable restriction is two pets per unit. Why two? Dogs, especially, and cats are social animals and they benefit from each others company, and are therefore less likely to be disruptive when their owners are out at work.
I heard recently about a dog that was in danger of being evicted from a unit block because of its barking when left alone – until its owners brought in a kitten for company.
If you are considering bringing pets into your block, remember that there may be owners and tenants who moved there because they didn’t want to be around animals.
But you can assuage a lot of concern by reminding people that even when animals have been allowed, they can be removed if they prove to be disruptive or even present a health concern for residents.