Crocodile

Okay, you are trying to cover way too much ground in way to little time.
If it was me, I would fly from Byron to Cairns - skip everything in between. That way you can see the reef, rainforest, Undara can be a side trip, plenty of other things around Cairns to have a great time for 2 weeks and you stay off the roads as much as you can. September is a great time in Cairns - basically it is 28C and sunny every day.

I would not recommend what you are wanting to do - spending long times on the roads is only asking for more trouble, especially if you are unfamiliar with the roads, the car and driving on the other side of the road. What is in Brisbane to see specifically - skip it? Fraser Island is a big island and not really suitable for a day - but it can be done in a long day trip with a tour group (4wd only). Cania Gorge - nice, but not nice enough to get me out there again. 1770 is a quiet little beachside town, but there really is nothing there. 1770 to Mackay is over a 6hr drive and there is pretty much nothing to see - between Rockhampton and Mackay there is nothing to see and is one of the more dangerous roads (fatigue). Don't bother with Mackay - go straight to Airlie Beach. But you will want to go to the islands anyway off Airlie Beach. Airlie Beach to Undara is a long way - 10hrs drive. Not alot to do at Undara, except for the caves. Undara to Cairns via Atherton is nice.

Driving long distances on holiday is not a great idea - you are tired, distracted and in unfamiliar surroundings. If you must though, get plenty of sleep and avoid driving at dawn and dusk because of livestock and kangaroos. Don't drive at night. Don't drive tired, please - that is one of the bigger problems on these roads.