Welcome to Melbourne, hope you have a great time.
If you don't mind a bit of a drive, I would suggest the Shepparton Motor Museum. (
http://sheppartonmotormuseum.com.au/) It has plenty of classic cars and antiques. I visited a few months back with my girlfriend (who isn't into cars) and we both enjoyed it, even though the cars were well before our time. I'd say its worth the time since enjoyed our afternoon and neither of us are super into cars, especially my girlfriend, but there's something cool about being around such old, classic cars.