Australian citizens and permanent residents can live with their foreign partners if they are able to secure an appropriate visa. Those who are successful in their application can avail of permanent residency for as long as two years. Note that Australian partner visas are applicable to a wide range of relationships including those who are legally married, in a defacto relationship (cohabited for at least one year), or in a registered relationship (living together, can be less than a year, registered in an Australian territory or state).
Temporary partner visas grant the right to travel and work in Australia, as well as access to Medicare. This will be valid until the decision for the permanent visa comes out after the usual 2 years. Couples who are in a long-term relationship can shoot for a permanent visa right away. To qualify, the relationship must be at least 3 years long. The minimum drops to 2 years if there is a dependent child.