["Cossack and Roebourne", The West Australian, Monday 11 May 1885, page 3]

...

Upon approaching Roebourne a stranger is struck with the peculiar aspect of the buildings, which are of a varied and motley description, and nearly all presenting a low squab appearance. They are chiefly of wood, with roofs of corrugated iron fastened down with stout battens firmly bolted through the rafters. Upon closer examination the rafters will be found bolted to the wall plates, and in turn the latter are clamped down to the uprights. When inquiring why such a quantity of iron is used, the reply is, "willy willy," the native word for cyclone, the meaning of which is very clear to all who have resided a few years in Roebourne. It is now over three years since the last severe willy willy passed over the town, and traces of the whirling blast may be seen in sheets of iron, crumpled up like brown paper.

AB notes:

A clear indication here of the origin of the expression "willy willy".