A better analogy would be ‘Australian buys Italian goods from online store in Australia’.
The entire point of the analogy is that we are eschewing "online" stuff so that we can see how "bUt On tHE iNTeRnEt" applies, so "but make it an online store" is literally missing the point.
Better analogy in that sense would be still "Australian sends an agent to buy something from a physical store in Italy after finding a printed catalog that a third party imported into Australia from Italy".