In Australian English, willy-willy (also whirly-whirly) traditionally refers to a dust devil — a small, short-lived whirlwind lifting dust/debris in the Outback. However, in some regions (especially tropical north), it's used colloquially for a tropical cyclone (hurricane/typhoon equivalent).
Clarification:
Official weather warnings use "tropical cyclone" (Category 1–5). "Willy-willy" remains a colorful bush term for both dust devils and, loosely, cyclones.