I agree, you can get some brilliant flying days over here during winter, but you can also get some frustrating ones too! The first couple of hundred miles north of Perth are nicest to see around September - everything is (hopefully) still green, the wildflowers are out, and the days are warming up but not too hot. Further north is nice most of the year, but again can be a little unpleasant during summer, especially in a light aircraft! Not too sure about the far north as never have been there! There are some beautiful places to see in the states south west, weather can be a little hit and miss but nothing too dramatic, especially if you've been flying in the UK. Around March could also be a nice time, though it's not uncommon to be still getting occasional 40 degree plus days at that time of year.
Have a great time - you'll love it!