It's not mentioned in my 'Oxford Companion to Australian Folklore' but it is in Bill Wannan's 'Australian Folklore'

Sir Robrt menzies in the course of his 1967Ditchley Foundation lecture, delivered at Ditchley Park, near Oxford England said: "There is an old saying in Australia, when a vital choice has to be made: Sydney or the bush. All or nothing, as you might say"
source - quoted in The Australian, (Sydney, 29th July 1967)

I tried to find a free searchable Macquarie Dictonary as I don't have an Australian dictionary, but can't find anything.

But Bob has lots' dictionaries!

Warren Fahey's site
There was a popular saying: 'Sydney or the Bush!' It was offered as almost a dare as if the two were miles apart – and, of course, they were and still are. Viva le difference! Sydney was also known as the city of four S's – Sea, Sin, Sex and Sorrow. There is much folklore surrounding bushies coming down to the 'Big Smoke' and, sadly, many of these trips were an extremely sorrowful story. It's true the cashed-up bush worker was occasionally 'lambed down' in the first or even second outback shanty he ventured into, but, in some ways, this was preferable to the 'lambing down' those who did reach the city often experienced, most of it self-inflicted! The reality is that many the isolated bush worker bolstered his (and sometimes her) routine boredom by thinking of the eventual 'great escape' to Sydney to 'live it up'. Tales were told and retold in the shearing huts, drover's camps and wayside shanties, of how the city 'eats bush people for breakfast' but this only added to their determination to experience for themselves. There are also stories of cityslickers venturing into the bush – an equally scary proposition for many the new chum.