Landlords have had various justifications in the past about why they won't allow pets as part of their lease agreements - some of them justified, some of them not. However, tenancy laws in some states regarding pets have changed, making it not only difficult for landlords to say no - in Victoria and the ACT for example, the landlord may end up at the tenancy tribunal in their attempt to refuse their tenants right to keep a pet.
If you're considering moving a pet into your rental property, it's important to do your research to make sure the kind of pet you get is compatible with the property you currently live in - unless you plan to move. For some animals an outside space is essential, and then there's a subcategory of those animals who need that outside space to be fully fenced. This keeps them AND passers-by out of harm's way. If you live in an apartment, and not on the ground floor, you'll need to think through the logistics of your pet not having outside space. You'll need a strategy around how you'll make sure it's well trained to do its business exactly where you want it to, if it doesn't have a garden or a courtyard to do it in.
Another good strategy is to think small - for pets that aren't cats or dogs, you may just need a nice corner to position a hutch or a cage in, that gets enough light and fresh air - so flats or units are fine. If you live in an apartment building, it's worth thinking about what kind of pets your neighbours have. Many of them will have already done the hard work of settling a pet into their home and could offer you some great tips about the kind of pet to choose.
Many new pet owners get so excited about the cute, sweet bundle of fluffy joy about to be theirs, that they neglect to properly understand the challenges that come with having a pet - especially a newborn one. A pet should tick the boxes of what you want, but also be selected with deep consideration around its behaviour and how that might affect the neighbours as it settles into to its new home. Make sure that whatever animal you choose, it will not be the kind to cause damage to property or create problems for other tenants or neighbours. If the pet you are thinking about is prone to poor toileting habits indoors, or scratching corners of furniture and surfaces, or barking, meowing, tweeting and squawking at all hours, before too long you may be looking for another place to live.
Even though landlords can't refuse your choice to have a pet, they can decide not to renew your lease if you choose to have a problematic pet move in with you. Talking with your agent before you choose a pet might give you some insights about the kinds of pets commonly chosen for rental properties. You can also talk to your agent about a 'pet lease agreement'. This exists in addition to a normal tenancy agreement at some agencies (and also have might vary from one agency to the next). Pet leases are usually about one page long and outline the landlord's expectations about the health, hygiene, and behaviour of your pet, ending in your signature. This is not a necessity, but it at least validates your seriousness about being a pet owner in the eyes of your landlord. It confirms your commitment to be responsible for the pet and to be sure it's presence in the property does not betray the terms of the pet lease agreement, just as a residential tenancy agreement does.
If you're moving and bringing a pet with you, as mentioned previously you can't be refused on the grounds of having a pet, but it may quietly influence the decision of the landlord without your knowledge. To counteract the possibility of this, try to be open and offer full disclosure in the application process. By declaring your pet's existence in a way that validates its importance to you, the landlord can choose based on having all the knowledge at hand, rather than a simple line item in an application that ticks 'yes' to the question 'do you have pets'.
One way to do this is to include a 'pet resumé' in your application. This may sound like a strange idea but just as you provide personal information about yourself on a residential property application, it can be very useful to include information about your pet too. A super cute photo might be nice, but also add confirmation from the vet that they have been tested and treated for pests, that all of their vaccinations are up to date and they have been spayed/neutered where necessary. A copy of any obedience training, or awards (such as pet shows, grooming, breed awards etc.) they have won could also be useful. If you have lived with the pet in a previous property, ask your last landlord to be sure to mention your pet, its good behaviour and the excellent condition you left the property in when vacating. Collectively these documents let the landlord know your pet is clean, healthy, will not spread disease, is well trained and cared for and ultimately will be a good 'tenant'. If you do get approval for a property and confirmation that your pet can also move in, make sure you get approval for your pet to be there in writing in case property management changes ownership and there are problems with your pet being there.