The Perth Gazette & Western Australian Journal is the earliest WA newspaper listed on Trove. In January 1833, it didn’t have a lot of advertisements. The second issue seems to have just three that aren’t government announcement. Mrs Barron’s ad above appeared the first page of that second issue, and the previous one as well.

Death of an Old Colonist.-By the death of Mrs. Barron, which took place at Perth on Saturday last, the colony is said to have lost the first white woman that ever stepped on the shores of Western Australia ;the first proud possessor of a cow, and the first person who baked a loaf of bread, in the colony.
The Westrn Australian Times, 26 February 1878