Green’s Dictionary of Slang

willie n.4

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

(orig. Aus.) a tantrum.

[US]Alt. Eng. Dict. [Internet] willie tantrum.

In phrases

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

(Aus.) to throw a fit, lit. or fig.

Cumberland Argus (Sydney) 15 Aug. 18/4: When forcibly about the street you rouse, / If when it’s dry your wife is driven dilly / Because the house is always full of dust, / And if sometimes you nearly throw a willie / When you consider things are so unjust.
[Aus]Truth (Sydney) 23 Nov. 3/5: A tote clerk at Rosebery yesterday almost chucked a willie at the window when an investor appeared and plonked down £100 in one hand. It was the biggest lump sum ever staked in on one horse in the history of the Rosebery Club, and possibly in all A.R.C. racing.
[Aus]Baker Popular Dict. Aus. Sl. 121: To throw a fit is [...] to throw a sixer, willy or seven.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 240/2: throw a willy – have a fit, as ‘I was so furious I almost threw a willy.’.
[Aus] ‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxiii 4/3: chuck a willy: Have a fit.
[Aus]N. Keesing Lily on the Dustbin 184: Family members [...] will long remember the day mum ‘blew her top’, ‘snapped her twig’, ‘popped her cork’, ‘did her block’ and ‘chucked a willy.’.