The Collaborative International Dictionary of English v.0.48:

Queerness \Queer"ness\, n.
   The quality or state of being queer.
   [1913 Webster]

WordNet (r) 3.0 (2006):

queerness
    n 1: a strange attitude or habit [syn: oddity, queerness,
         quirk, quirkiness, crotchet]
    2: a sexual attraction to (or sexual relations with) persons of
       the same sex [syn: homosexuality, homosexualism,
       homoeroticism, queerness, gayness]