Whimsy is, sadly, not a commonly used word in American English. It is a great, fun word. It makes me think of "whimsical"; "a lark"; "on a whim"; "capricious"; "spritely"; "elfish"; "playful"; "light-hearted fun"; "following a sudden impulse to do something fun and unexpected".

It is common enough to use in conversation where appropriate. I think the adjective form, "whimsical" is more common than the noun, "whimsy." To me, "whimsical" means imaginative, like something from a dream or a fantasy. It does connote lightness, airiness; not tied down by logic or reason, but in a positive way. To use it in a sentence: This children's book about a boy's adventures with a unicorn is quite whimsical.

It's common to me. :) Whimsy is behaving on a whim (a caprice). Sometimes I make choices out of whimsy. I'm not so predictable.

Whimsey used to be used a lot on American decorating shows, but I think those shows have moved away from it. Raja gave some good synonyms that are more often used.