A girlfriend and I did it way back in the 70's, two up on a Kawasaki Z1 with all our luggage in home-made panniers and luggage rack. Probably not the ideal bike, but I was in my 20's, indestructible and too stupid to know better back then. I suppose a Beemer would have been a better choice, as would separate bikes for me and the lady friend, but the Kawasaki was what I had at the time and she didn't ride. Being so overloaded it was a handful on the bulldust road sections (Port Hedland to Broome was 600 km of dirt, loose sand, bulldust and huge mud bog-holes in those days). We went clockwise around. Bike ran flawlessly until the frame broke below the headstock. Musta been the rough Queensland roads from the NT border to Townsville. Never seen so many massive bumps and potholes before or since. Probably all nice smooth highway now. Got the frame welded up in Mackay and continued on down the east coast.
If I were to tackle it again I'd take something a bit more comfortable than a Z1. Highway 1 is sealed all the way now, so there's no need for one of those big chook chasers. A good road bike would be the go, and weight isn't such an issue when on the move. As long as it's not too heavy to pick up when it falls over (and it will fall over). I reckon I'd choose a bike that's fixable in the middle of nowhere. For me, that would probably rule out anything with a computer and massively complex wiring. I'd rather not fork out big handfuls of money on a truckload of diagnostic gear and possibly a spare ECU. Carbies are old school but simple. A Laverda RGS might be comfortable enough for long days in the saddle (never ridden one so I dunno). Or maybe an airhead BMW or a Guzzi.
Actually. If I were to head off tomorrow, I'd be tempted to take my Kwak Z1300 outfit. It has a pretty much bulletproof engine and can carry loads of gear. There's plenty of room in the sidecar for tools, spare parts, fuel cans, water, and if that's not enough it can also tow a trailer. It won't fall over, and has a big plush seat that's quite comfortable to sit on for hours on end. While it does have fuel injection and an ECU, it's pretty crude and basic. You can actually open up the ECU and inspect/repair the printed circuit board (been in there and done that before). I also know where I can lay my hands on a spare ECU for peanuts. Only disadvantage of the old Kwak is that it's very thirsty on fuel.