Wouldn't "What should I do to live on an island?" be better? From what I know it's "to live ON an island" and secondly the Italian text doesn't mean "how can I live on an island" but more something along the lines of "what should I do to..."... maybe even "what to do to live on an island?"... At least that's how I see it.
The sense of the text is of someone being imprisoned inside him/herself and willing to be free and experiencing a fairy tale. This is I think the reason for using in(inside) an island instead of "on an island" that would be the correct preposition in a common context.