Very innovative and commendable idea, but unfortunately didn't have much fun playing it myself.
Figuring out where the next key was located (without hints) essentially came down to noticing something arbitrary (like number of empty slots) as opposed to actually finding a solution. In a similar vein, I would've liked to see the jumping to earlier levels used in a more meaningful way (e.g. doing something in one level affects something in the subsequent levels).
The music was very nice, though. Very cute and relaxing!