There were no structures, buildings, or any sort of a human settlement in Antarctica that they could use as the basis of an ice trade industry. And by the time of the Heroic Age of Antarctic Exploration, people were able to make their own ice in Australia (and elsewhere) using mechanical refrigeration.
Boston was the centre of the international ice trade, with Wenham Lake Ice Company, trading on the name of a Massachusetts lake particularly renowned for the purity of its water. Source
As those articles say, one of the first ice-making machines in the world was invited in Geelong, Australia by Scottish-born James Harrison in 1851. Or rather, he improved upon an 1834 British design for vapour-compression refrigeration.
stumcm OP t1_ismey9y wrote
Reply to comment by [deleted] in TIL that before the invention of regfrigeration in 1851, ice had to be imported to Australia from Boston, Massachusetts. The ice blocks travelled through the tropics inside ships insulated with timber, straw, peat, and sawdust by stumcm
You dispute that Australia needed to import ice from overseas before 1851?