Unknown. Possibly (putative obsolete brand of roll-your-own tobacco) + -y.
David Bradley, Australian Journal of Linguistics (1989) suggests that it may be derived from a widely used brand of loose tobacco used for roll-your-owns, Bull Durham, clipped and resuffixed with the most productive suffix for forming new colloquial words in Australian English.
Suggested that it was a term brought back from ANZAC forces as a Dhurrie Rug and a cigarette are both rolled.
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