The Collaborative International Dictionary of English v.0.48:

Left-handedness \Left"-hand`ed*ness\, Left-handiness
\Left"-hand`i*ness\ (-[i^]*n[e^]s), n.
   The state or quality of being left-handed; awkwardness.
   [1913 Webster]

         An awkward address, ungraceful attitudes and actions,
         and a certain left-handiness (if I may use the
         expression) proclaim low education.      --Chesterfield.
   [1913 Webster] lefthander

WordNet (r) 3.0 (2006):

left-handedness
    n 1: the status of being born of a morganatic marriage
    2: preference for using the left hand [syn: left-handedness,
       sinistrality]