A couple obstacles I see with this idea:
1) An island doesn't really lend itself to the idea of infinite exploration. If you're on an island, you'd expect to eventually be able to walk from one shore to the other. It would be more plausible if you were lost on an uncharted continent, or maybe in an archipelago.
2) If your child keeps the same abilities, what is the consequence of dying? The way death is handled is (IMO) one of the essential qualities of a roguelike.
3) Metroidvania games typically have some type of lock-and-key system that guides the player through the game world. You need powerup A to get into the area that contains powerup B, which you need to get into the area that contains powerup C, et cetera. While it would certainly be possible to randomly generate level structures that enforce this constraint, extending this pattern indefinitely could be difficult without making the powers totally arbitrary. Getting to new areas by using the "double jump", the "power glove", or the "fireball" is interesting because each ability continues to serve a purpose in gameplay after reaching the new area. If these "key" powerups were randomly generated, you'd either have to mix the functional ones with non-functional ones (that is, powerups like "yellow keycard") or give the game a more linear structure--one in which the main obstacle preventing you from entering an area is safe passage through the previous area.
You might also consider looking at Spelunky for inspiration. It's one realization of a randomly generated platformer.