It's not exactly a historical journal, but given we're discussing the history of a pop culture icon it qualifies as a reasonable source I think. A Guy, a Palm Tree, and a Desert Island: The Cartoon Genre That Just Won’t Die

The article recounts that the desert island cartoons you're describing were made famous by the New Yorker in the 1950's, with 1957 being their most popular year. The article describes the cartoon trope having most likely arisen in the 1920's or 1930's, in the magazines that predated the New Yorker, Judge and Life. Both of which had witty single frame cartoons within their pages.

The idea of a desert island in literature is far older. Shakespeare used a desert island in The Tempest (1610) and some much earlier arabic/moorish literature by Ibn Tufail uses the idea as well.