Please note that some international airlines will have an agreement where they will transfer your luggage from one airline to another. If your flight is on two separate tickets some airlines will require you to collect luggage and check it in again for the second part of your flight.
If you are unsure on what the procedure will be you can call the airline direct or ask them when you check-in.
For domestic travel within Australia, your luggage will not be transferred from one airline to another (for example, Virgin Australia to Qantas). You will have to collect your luggage from the first flight and then check-in again for the next sevice. Also, you will need at least 90min connection time between the two different carriers to ensure there are no problems.
Please contact the airline direct for any complicated requests.