'Australian & Melbourne Distilleries' were two separate companies. The Official Record describes them jointly as the Australian Distillery Company, Melbourne (p.902), although the medal uses the longer name.
Sands & McDougall's Melbourne directory for 1879 lists the Australian Distillery Works at Yarra Bank South, with H.J. Browne as proprietor; Melbourne Distillery Company was located at Easey St, Collingwood, with J. Hugh as proprietor. Interestingly, the medal refers to the 'proprietor' of the Australian & Melbourne Distilleries, implying that the two businesses had a single proprietor, although this is not borne out by Sands & McDougall.
The Australian Distillery Co. Ltd was de-listed on 26 May 1966, when it was taken over by Equity Management Limited.
Delisted Company website http://www.delisted.com.au/CompanyDisplay.aspx?ID=2215&Company=, accessed 9/2/2004
Sands & McDougall Melbourne Directory, 1879.