Source: Consumer Affairs Victoria
In Victoria, there are no laws that directly cover pets in tenancies or residencies. However, it is possible to include a clause that bans pets in a lease. A prospective tenant could accept, reject or negotiate such a clause.
If a tenant or resident has a pet or intends to get one, they should get permission from the landlord or owner and include the permission as a term of the tenancy before moving in.
If their pet has caused damage or nuisance, or the property has not been kept in a reasonably clean condition because of it, a tenant or resident may be issued a Notice for breach of duty. This notice may require the tenant or resident to fix the damage or ensure the nuisance or poor property condition does not happen again. If there was no agreement for a pet to be kept, this notice may also require the tenant to remove the pet.
However, a landlord or owner cannot serve a tenant or resident with a Notice for breach of duty simply for breaking a ‘no pets’ clause in a tenancy agreement, if there has not been damage or nuisance.
If you rent an apartment or unit, there is likely to be an owners corporation that manages common areas such as gardens, driveways and foyers. An owners corporation may have its own rules about pets, which tenants and residents must abide by.
Landlords or owners should give new tenants or residents a copy of the owners corporation rules at the start of their tenancy.
Assistance animals are not pets, but rather are highly trained disability support services that enable a person with disability to safely participate in personal and public life activities.
https://www.consumer.vic.gov.au/housing/renting/applying-for-a-rental-property-or-room/pets-and-renting