Because 1) Australia was an English colony and they would have been subject to arrest and trial there, and 2) nobody in the party would have been able to survive there. And they didn't want to live in such a place, what every one of those men and women wanted was something as close to the island paradise of Tahiti as they could get - but all the most paradisical island had people already living there. Pitcairn was the best they could do.
As to whether they might have headed for the Americas... no. For one thing it was too far, and if they traveled in the usual shipping lanes they'd probably have been identified, and if they traveled outside the normal shipping lanes there was a risk of a disaster at sea. And all the coast of the Americas were settled, almost entirely by citizens of nations who had armies and navies of their own, and who wouldn't want any members of their own armies or navies to get the idea that mutiny was a good idea. No, if the mutineers had been identified by the authorities of any nation in that region, even one that was hostile to the British, they'd have been imprisoned or hanged for their crimes. So yeah... Pitcairn really was the best they could do.
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