Have a look the numerous other threads on Au trips, including a few down the page.
Australia is not about the cities. Its about the areas out of the cities. A city is a city is a city. They all have a lot of boring Toyota's, just like your home town/city,

3 weeks is a just reasonable time. Does the 3 weeks include your travel time from/to home? You will not do much on the day of arrival & day of departure

Forget Brisbane for 4 nights. 1 night is too much
Surfers Paradise for 4 nights. Ughh. Its very commercialised. And about 60-80minues drive from Brisbane.

Cairns 4 days. Ok, 5 would be better. A good time of the year to be in FNQ

Darwin. Go out to Kakadu for several days. And other national parks in the area. Darwin is different

But best if all you can attend Oz Fest 14 Newcastle, just north of Sydney. @:-) ^
You can learn a lot about Aussie from some people who travel Au frequently and from some locals (better than 4/4 days in BNE/Surfers, but that is not hard)