Green’s Dictionary of Slang

willie n.4

[? willies n. or abbr. SAusE willy, a whirlwind or link to SE willy-nilly]

[1940s+] (orig. Aus.) a tantrum.

In phrases

chuck a willie (v.) (also chuck a willy, throw a willy)

[1920s+] (Aus.) to throw a fit, lit. or fig.