Darwin > Syd
I've been around both areas. The southern area as a kid, and have lived in far north Queensland all my life.
My opinion may be biased, but I reckon from NT to Qld will be the most stereotypical Aussie setting you will see.
Darwin-Syd you will get to Cattle stations, crocodiles, kangaroos, warm weather, ULURU, great fishing wicked camping, massive red canyons/gorges, see beautiful beaches/islands and the Great Barrier Reef/whale watching, meet aboriginals, and depending on your persona, may be invited to partake or learn in activities and their culture. I grew up in Bamaga (northernmost point in Aus) and was an unreal experience. Google 'barramundi', Mission Beach, Whitsundays, Great Barrier Reef, Uluru (Ayers Rock). On top of that the cattle stations out west provide some great dirt riding, and amazing country folk with fantastic stories and warm hearts. We go bowhunting out by Croydon yearly on cattle stations there and the countryside is fantastic. Plus its closer to ship to Darwin
I think the Perth-Syd route would also be nice, but you will miss A LOT (both ways of course). You would get to do the Great Ocean Road, see the 12 apostles, but after that its a lot of sheep farms and grain fields, and chilly/possibly wet weather. Unfortunately I can't elaborate too much here, but I'm sure someone else can sell the south...
I'm definitely biased...but I feel for a good reason
Good luck and feel free to contact for more info.