I think you are over worrying about it. If you get to the airport by 7:30, you have plenty of time to catch the flight.
Journey time out to Tullamarine from the city is not very long; leave a CBD hotel at 6:00 and you will be fine , get there at 6:30 and just be getting bored sat at an airport waiting 2.5 hours for a flight
Yu can use the self service passport control
From
https://www.border.gov.au/Trav/Ente/...rtureSmartGate
Originally Posted by Department of Immigration and Border Protection
Departures SmartGate can process all travellers, regardless of age, nationality. They can process ePassport and non-ePassport (providing it is a machine readable passport), as long as travellers are able to understand and follow the process without assistance.