The Collaborative International Dictionary of English v.0.48:

Gilbertian \Gilbertian\ prop. a.
   1. Of, pertaining to, or characteristic of the style of
      William S. Gilbert; as, Gilbertian libretti.
      [WordNet 1.5]

   2. Wildly comic and improbable, as in Gilbert and Sullivan
      operas; as, Gilbertian coincidences.
      [WordNet 1.5]

            a Gilbertian world people with foundlings and
            changelings.                          --T. C.
                                                  Worsley
      [WordNet 1.5]

WordNet (r) 3.0 (2006):

Gilbertian
    adj 1: of or pertaining to or characteristic of the style of
           William S. Gilbert; "Gilbertian libretti"
    2: wildly comic and improbable as in Gilbert and Sullivan
       operas; "a Gilbertian world people with foundlings and
       changelings"- T.C.Worsley