As many others have said Melbourne International and Domestic are in separate but connected terminals. If you arrive at the airport at 6.30 for a 9.00 flight you should have plenty of time to check in and enjoy the FLounge.
Staying at an airport hotel will take the worry out of early departure.
The hotel connected to the terminal is the Parkroyal, not the Regent, and convenient to use.
The Holiday Inn is also relatively close to the terminal. Can be walked or there is a dedicated Hotel Shuttle.