With all Australia has to offer, and such limited time, I'm concerned you may be spreading yourself too thin.
At the least, I cannot fathom a full week in Sydney; not when you only have three with which to work, and are looking at both NZ and Aus.
Australia, generally, is not the place to go for world class luxury, IMO, with perhaps an exception or two (e.g. Saffire or COMO Perth). Of course NZ has a plenitude of wonderful lodges.
May I suggest, unless you're just hell-bent on going to both countries, picking one and dedicating three weeks there?