The Collaborative International Dictionary of English v.0.48:

Desirability \De*sir`a*bil"i*ty\, n.
   The state or quality of being desirable; desirableness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

desirability
    n 1: the quality of being worthy of desiring [syn:
         desirability, desirableness] [ant: undesirability]
    2: attractiveness to the opposite sex [syn: sex appeal,
       desirability, desirableness, oomph]