They set out from Geraldton, some ways north of Perth in Western Australia (itself known as the remotest major city on earth!) and travelled north and east along the coast of Western Australia, until they made Darwin and headed south to Alice Springs. Theirs was a hitch-hike somewhat removed from the classical images. There were no roads much of the way after all, just beaten tracks that caused so much trouble in the crossing that traffic was not a thought you'd tie to them. Traffic? What traffic? No, people travelling on these routes were so rare, that the only way to traverse them was to ask around town, get to know the locals, until you found someone, usually a truck, a policeman or an engineer of some sort, planning a trip. Even then on the first leg to Cornarvon Coralie had to fly, while Leslie rode on a banana truck, there just wasn't any other realistic option!
Well, the Rees were on a mission, so to speak, to explore life in the outback, and if you'll pardon the pun, on the missions. They weren't especially religious and arrived at the many missions with a sceptical eye. These were outposts of church where an attempt was made at educating and integrating Aboriginals with the ever encroaching pastoral Australian, and proselytising didn't appear to be high on the agenda at all.
The sensible option was of course to fly. In fact that's how most people travelled, as there just weren't any roads to speak of let alone a public transport system. The wanted though to stick to the ground, to experience the outback and to feel it, and while they make not explicit mention of it I suspect hitch-hiking was their way of, at once shirking the responsibility for transport (these "roads" needed serious vehicles, and good emergency gear) and winning exposure to the culture (the people of Western Australia). And hitch-hiking has shirking responsibility and exposure to culture written all over it after all ...