Australia for 21 days in November

I’d skip driving from Sydney to Melbourne and spend more time in Victoria especially driving the great ocean road

Brisbane and the Gold Coast are with your time

Lived in Brisbane for a little over 2 years so was able to travel extensively throughout the country. Of all those things you mentioned, I'd honestly skip Alice Springs. I rented a camper van with some friends and drove from Adelaide to AS and while that trip was very enjoyable (because of the company), AS is pretty unremarkable. They have Uluru (Ayers Rock) which is just something to check off the list of places to be seen, but I wouldn't go out of my way to visit AS.

Visiting Cairns for the Great Barrier Reef is a must. It's continues to shrink and die at a rapid pace, so you must visit while you can. I also recommend going with a company that goes pretty far off the coast. If you stay too close, the water can be quite dirty on some days and the clarity is not the best. Overall though, absolute must place to stop. There's even a sign in the water that shows where Steve Irwin was stung by the sting ray. It's remarkably close to shore in a canal.

I loved Darwin as well and visiting Kadadu national park. You have to be careful going for a swim in the swimming holes are there are crocs everywhere (and believe me, those post signs saying DO NOT SWIM!) but what's the fun in that?! Looking back it was quite idiotic, but hey I'm still here to tell the tale.

I could go on and on about Aus, I love that place like a second home. I'm happy to answer and specific questions you have, places to visit, etc, just keep them coming. As someone else said, Great Ocean Road is amazing and you can really do that in just a day or 2. They've even got some nice wineries in Adelaide if you have time there. Catching a footie game (Aussie rules football) should be something to do as well.