Green’s Dictionary of Slang

doughy n.2

also doughey
[play on the ‘doughy’ consistency of the buttocks, i.e. the body’s ‘end’]

(Aus.) a cigarette end .

[Aus] ‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxiv 4/3: dog end: English for bumper, fag end, doughey, Victor Trumper.