The Collaborative International Dictionary of English v.0.48:

Prickliness \Prick"li*ness\, n. [From Prickly.]
   The quality of being prickly, or of having many prickles.
   [1913 Webster]

WordNet (r) 3.0 (2006):

prickliness
    n 1: the quality of being covered with prickly thorns or spines
         [syn: prickliness, bristliness, spininess,
         thorniness]