Unlike other cities, in Melbourne, on Metropolitan trains, trams and buses
If your animal isn’t a guide dog, hearing guide dog or guide dog in training, and doesn’t have an Assistance Animal Pass, it may still be able to travel with you on public transport.

Small animals can travel with you on trains, trams and buses in a suitable animal container.

Dogs can travel with you on trains, as long as they’re on a lead and wearing a muzzle. If you bring your dog on a train you must:

clean up any mess your dog makes
make sure your dog doesn’t sit on seats, or block aisles and doors
keep your dog under your control at all times
avoid travelling on weekdays between 7am and 9am or 4pm and 6pm.
Animals other than those in a suitable animal container, or dogs on a leash and wearing a muzzle, are not allowed on trains. Only animals in a suitable animal container are allowed on trams and buses. 

V/Line trains and coaches
You can bring small animals on V/Line trains in an suitable animal container. Suitable animal containers must:

be no more than 56cm long, 30cm wide and 38cm high
weigh a maximum of 15kg, including your animal
allow your animal space to comfortably stand up, lie down and turn around.
Only one container is allowed per customer.
You can put your animal container in the luggage van of Loco-Hauled trains or inside the passenger cabin or bike and luggage storage area of VLocity and Sprinter trains. V/Line conductors will confirm if there is enough space for small animals.

When travelling with an animal on V/Line trains:

clean up any mess your animal makes
avoid travelling on weekdays between 7am and 9am or 4pm and 6pm
don’t bring any dangerous animals on board
Animals are not allowed on V/Line coaches, including rail replacement buses, unless they’re a guide dog or have an Assistance Animal Pass.

For more information, visit the V/Line website.

It would be excellent if the same rules existed in our other major cities within Australia.