Green’s Dictionary of Slang

molly (the monk) adj.

[rhy. sl.]

(Aus.) drunk.

[Aus]Argus (Melbourne) 13 June 4s/2: If, however, he consumes too much ‘pig’s ear ’ or ‘thick and thin’, he may finish up mollies [...] contracted from ‘mollie the monk’.
[Aus]Kings Cross Whisper (Sydney) xxvi. 6/1: Now the basic type of booze, and that which induces the most popular result (gets you molly the monk) is – wait for it – beer.
[Aus]Kings Cross Whisper (Sydney) cliv. 2/4: Ophelia was more than a little bit Molly the Monk after Parkinson had been loosening her up a bit with three bottles of Quelltaler hock.
[Aus]J. Byrell (con. 1959) Up the Cross 19: [T]hey should escort the three-quarters molly-the-monk Whiffy Maloney back round the corner.
[Aus]J. Byrell Lairs, Urgers & Coat-Tuggers 61: Big Oscar wasn’t molly or even half blotto because he’d only sunk three schooners.