Since “desert” in this sense means “deserted” (isolated, uninhabited) and not “like a desert” (an arid region of sand and little vegetation), I assume there’d be a water source and growing things.
In that case, a sharp hatchet, a length of sturdy rope, and dry matches.
It would also be nice if the currents would bring me a trunk containing books, paper, pen and ink, blankets, a change of clothes, extra underwear, a cup and bowl, a spoon, a cooking pot, a teakettle, some tea, a Coleman lantern, a comfortable chair, some mosquito netting, aspirin, soap, a comb, and a toothbrush.