No, no, definitely no. Forget it. It is completely unworkable.
On the other hand, MEL is an absolutely lovely, lovely city and you can walk around and have a grand day along the river, or whatever. There's tons to do.
Great that you are so into AUS and you'll have a lovely time doing all of these things you've missed on your next trip down.
Heck, we usually go down there every year.
PS: you don't need a driver in MEL, just get in the car and drive. But not this time. Cab, walk, boat, have a great time!