When you're visiting Melbourne - and Australia in general - earthquakes are not high on the list of things to be prepared for. However, last night (March 7th), Melbourne (and surrounds) showed itself to not be completely impervious to the phenomenon.
Not having previously experienced an earthquake, I didn't realize what was going on when I first felt the rumbling and heard the clatter of everything in the flat vibrating. However, it didn't take long for SES (State Emergency Services) to be notified and people to be talking about what happened - especially those people closest to the epicenter of the quake.
As of this morning, the quake is a 4.6 or 4.7. You can see the epicenter in relation to inner Melbourne and all the affected areas on a map on this news report.
So, while you're not likely to experience an earthquake in Melbourne - this is the first of this magnitude this close to the city since 1973 - don't rule it out as an impossibility.