Really depends on your suburb. Your water company will have very detailed reports on their website for your suburb, so you'll be able to see the hardness, as well as a bunch of more worrying contaminants.
Generally speaking, Melbourne water quality is pretty good, but it does vary. Also, just because the readings for your suburb are good (eg low hardness), that's no guarantee that the water on your street will match that good reading.
You can test for hardness by sending water off, one of the CS sponsors (Bombero) specialises in this stuff.
Ultimately, filtering your water will make your coffee taste better, but if the water is good to start with then the improvement will be small. On the other hand, if your water is bad, such as in Perth, the improvement will be enormous, literally huge.
I'm just skimming the surface here as this is a big topic. Other considerations include how often you rescale your Silvia. I used to do mine every 6 months, and the water where I live is quite soft.
Then there's the issue of having water that's too soft. Not an issue with tap water, but I believe that using pure water isn't recommended, again Bombero's site will explain this much better than I can.