3 weeks is a lot of time, you have plenty of options. If you're looking for a detailed itinerary, you might want to contact a travel agent that specializes in Australia.
Otherwise, if you're exploring on your own, there are two main routes that might be interesting. The first would be to go from Darwin
and Port Douglas
to see the Great Barrier Reef first, then continue down to Sunshine Coast
You could also take a Southern route straight down through Alice Springs
, hopping over to Kangaroo Island
, then continuing on to Melbourne
and visiting Tasmania
, finally up through Sydney
and to the Gold Coast
Really, with short domestic flights on Qantas or another airline, you could quickly get to each major city and spend 3-4 days at each stop to explore different areas. A travel agent could suggest specific hotels and attractions and customize it to your preferences.