Contrary to the thinking of the majority here, I think choosing a member of the opposite sex for this purpose is a really bad idea, especially if you have romantic notions in your mind.
You know nothing about this person other than their personality type! There might be a huge age discrepancy. They might be really ugly or otherwise nasty. You might be super unattracted to them, but that would not stop them from being attracted to YOU necessarily. And here you are trapped with them on a desert island for years, possibly, with no other company whatsoever.
This could be awkward and miserable, methinks. Consider, people, before you make the worst mistake of your life!
So, I would choose another female. Probably an INFP, since I have great conversations with them. It seems as though this island would not be too tricky to survive on, having all this food and fresh water and all, otherwise I might pick an ISXP to help with survival.