hi Willimstown,
I just purchased a single phase 14.5kW cooling/16kW heating Mitsubishi inverter ducted system. Its the largest of the single phase units. Cost me around the $10k mark and it runs beautifully. Very quiet and easy to use. I was actually talked out of purchasing Daikin. The installer told me they used to be good but turned bad a few years ago. Apparently most of the call outs he has with problems on newer systems (2 years or less) are mostly Daikin. They have dropped their quality. He recommended Mitsa by far.
If you're goint to stay in your place, it would pay to install gas heating also. Its a hell of a lot cheaper to run. Much cheaper!
I don't know why they've quoted you on a 20kW heating system. How big is your house? General rule from my research suggested 1kW for every square of your home...but there are many considerations to take into account of course. If you're interested in the mob I used, let me know. These blokes were really down to earth and actually went out of their way to help me save money on the installation, which is something you don't find much of anymore.
Dan.