Agriculture developed independently and at around the same time in Australia, Papua, the Americas and the Far East from what I have read.
That it happened to lead to civilization in the ancient Near East is I believe to do with the requirements of hosting agriculture in such a place. Max Weber says a fair bit about this - building the irrigation canals in Mesopotamia that were necessary for agriculture meant people had to band together under leaders and develop a system of almost slave labour. This process didn't happen in places that could rely on rainfall etc.
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