I know checked luggage goes straight through, but how long in advance do I need to be at the Melbourne airport?
The first leg is a domestic flight. Melbourne and Sydney are both in Australia. You should allow a few minutes of extra time for a passport and visa check which might be carried out at Melbourne, but apart from this it is no different than any other domestic flight. I would say arriving at the airport 60 minutes before departure is more than sufficient, 90 minutes if you are of the nervous disposition.