I guess it would be me and my faceless, Escapist issue shadow. I would hope something without a mouth needs no air or food or I'd be forced to eat her when she keeled over a minute after we suddenly popped onto the island.
The scale of the island suggests a rocky crag with no food, so my basic caloric needs would go unsatisfied unless there was an unlikely concentration of energy dense starch- for example tapioca plants (a Polynesian staple) and the means to render the starch non-toxic. Or bread fruit, which I would have to eat five cups worth to get my daily needs met. However that island isn't big enough to hold much.