The Collaborative International Dictionary of English v.0.48:

Curiousness \Cu"ri*ous*ness\, n.
   1. Carefulness; painstaking. [Obs.]
      [1913 Webster]

            My father's care
            With curiousness and cost did train me up. --
                                                  Massinger.
      [1913 Webster]

   2. The state of being curious; exactness of workmanship;
      ingenuity of contrivance.
      [1913 Webster]

   3. Inquisitiveness; curiosity.
      [1913 Webster]

WordNet (r) 3.0 (2006):

curiousness
    n 1: a state of active curiosity [syn: curiousness,
         inquisitiveness]
    2: the quality of being alien or not native; "the strangeness of
       a foreigner" [syn: foreignness, strangeness,
       curiousness] [ant: nativeness]