It's Melbourne, so fortunately the airport isn't too big (compared to the separate terminals for Sydney several km from each other).
If it's on the same ticket, no need to worry, Qantas will help you out. You'll land from Adelaide at Terminal 1 (Qantas), and will need to walk off the plane, out the gates, and across to the International departures.
If you're already checked in from Melbourne, you'll have a boarding pass already. If not you'll need to get one.
Then you go through passport control (3-5 min if you are able to use Smartgate - ie if your passport has a chip), and security (metal detector etc) - 5-10 min. At that point it's just a matter of walking to your gate - which in a hurry shouldn't be more than 5-10 minutes.
If you're going to miss it because of a late arrival, speak to the crew on the flight, and they may be able to advise. If it's on the same ticket, Qantas will help out and rebook you and make sure your luggage doesn't get misplaced. In theory ;)