I often arrive at MEL at about that time, or a little earlier, for international flights at 9:05 or 9:40.
The road traffic to the airport can be conjested, which is why I arrive early. If I left home 15 minutes later would arrive at the airport 30 minutes later.

Domestic & international security are separate. If it take 15 minutes for security & emigration that is a long time. Normally is quicker. But I have an e-passport so use the smartgate kiosks. Have not talked to a border official for a few years.
http://www.border.gov.au/Trav/Ente/Goin
In first you should get an express pass, but will not speed up the time much. When given these I do not use them.

Not many hotels at/close to the airport, but still a good idea to stay at an airport hotel.