First, let's be clear about the purpose of the CPI. In principle I believe that measuring the price level is impossible as the type and quality of goods and services in the economy changes constantly. However, some indicator about the changing cost of living is still important for determining changes to welfare payments and calculating real growth in incomes.
I will be interested in the outcomes of the current CPI review to see whether they improve or degrade this key national economic measure.
The ABS produces an Analytical Living Cost Index (ALCI) here, using the appropriate outlays method. Unfortunately, while interest rate are factored in, the price of home purchase is removed
the ALCIs, the changes in the amount of interest paid on mortgages (measured as part of financial and insurance services) and other costs (e.g. maintenance costs and council rates) are included for owner-occupied housing. In addition, changes in rental are measured for that part of the reference population that resides in rented dwellings. The ALCIs do not include the net purchase of housing and the increase in volume of housing due to renovations or extensions.
Furthermore, most other components of this measure are simply taken from the CPI in their quality adjusted form. Which gives the ABS an ALCI which mirrors CPI almost exactly.