Recently ran tests on water that had been passed thru a water filter. I can now scientifically say that these filters do 4/5ths of F.A. My analysis showed that less than 5% of trace metals were removed (Ca, Mg, Na etc)
As Kev said, the carbon filters are designed to remove organic compounds that impart odour and flavour. They reduce the chlorine levels but not chloride. Its important to understand the difference between chlorine (Cl2) and chloride (Cl-).
The best bet is to start with rain water which you can boil if you have issues with over hanging trees, or plane drop out. Using a program like beersmith you can calculate how much of each salt you need to add to adjust to your desired water profile. Or use spring water or RO water. Melbourne tap water is good as i said before, my experiences of Sydney water are that it is soft(ish) but tastes almost as bad as Adelaide water.
A good link to water profiles of the brewing world can be found
here
Hope that helps
DrSmurto