The Collaborative International Dictionary of English v.0.48:

Inquisitiveness \In*quis"i*tive*ness\, n.
   The quality or state of being inquisitive; the disposition to
   seek explanation and information; curiosity to learn what is
   unknown; esp., uncontrolled and impertinent curiosity.
   [1913 Webster]

         Mr. Boswell, whose inquisitiveness is seconded by great
         activity, scrambled in at a high window. --Johnson.
   [1913 Webster]

         Curiosity in children nature has provided, to remove
         that ignorance they were born with; which, without this
         busy inquisitiveness, will make them dull. --Locke.
   [1913 Webster]

WordNet (r) 3.0 (2006):

inquisitiveness
    n 1: a state of active curiosity [syn: curiousness,
         inquisitiveness]