The recent Queensland ruling that you quoted has been overturned by a Referee (whatever that is).
I think in your case, all you can do is wait and see what the other owner is going to do, and decide if you want to keep the by-law and “dare” them to bring in an animal.
Even though I am pro-pet, I am also pro-community and if a small community such as yours is against pets, and will be directly affect by their introduction, then I think you should have the right to continue to say no.
Is is not “unconscionable” and “discriminatory” for people who don’t want to be around animals to be forced to put up with them because one person has chosen to ignore by-laws that were in place long before he or she bought into the scheme?