Neil Said:

Has anyone recently road-tripped around Australia?

We Answered:

First, I have not done that exact trip, and can only respond to the question based on other travels around Australia. '

I would not consider doing the trip alone, under any circumstances. Travel the route you have suggested in a well equiped Ute. Carry water and Petrol.
Assume you are going to have problems finding both going from Mt Isa to Uluru, although you probably will not. Err on the side of caution. Fill with petrol every chance you get on the outback portion of the trip.
Budget 100 a day plus petrol. camp with a tent most of the time, but settle in to a pub on occasion for a beer and a shower. Allow a minimum of 30 days, and enjoy!
book your ferry crossing to KI well in advance, and be aware that it is pricey to take your vehicle to the island.