Monthly plans (also known as SIM Only or BYO Phone plans) work like regular phone plans, but without a lock-in contract.
These plans have a 30-day expiry and come with a set of inclusions that you agree on when you sign up. Every month your telco will bill you and automatically refresh your inclusions.
You need to bring your own phone to a Monthly plan. Happily, all of the Australian networks work on similar radio frequencies so you should be able to bring the phone you already own to any new phone plan you find in your search.