I think you are stretching it a bit to do multiple locations in Oz, NZ and HK all in 3 weeks.
Best to factor in a day or so to recover when you arrive although if you stopover in HK on the way this will help.
Don’t underestimate how long it takes to get around, it’s a huge country. Internal flights can be pretty cheap though so flying about is not too bad.
The last few times we flew to Oz we used the same travel agent and every time they either got us a better deal on flights or better flight times/stop overs. I dont think I would bother trying to do it myself any more.
Weather in NSW/QLD should be pretty nice, but Melbourne could be anything from spring-like to freezing and wet!