The closest match found for this business is 'Millar and Dismorr, Drapers etc., 43 Collins Street East' in Butterfield's 1855 Melbourne directory. John Hope found one other reference to the business, under the name Miller &; Dismorr, at the same address, in 1856.
Their tokens were struck by the Birmingham firm Smith and Kemp. Given that they were only listed in two Melbourne directories it seems likely that their tokens were issued between 1854 and 1856.
No other references to this business have been located.
Sharples, J. (1993). 'Catalogue of Victorian Trade Tokens.' Journal of the Numismatic Association of Australia. Vol.7. December, p.51.
Butterfield J. (1855). Melbourne Commercial Directory for 1855.
Hope, John (2005). 'Miller & Dismorr', unpublished MSS, 2005, 2pps.