The Collaborative International Dictionary of English v.0.48:

Rashness \Rash"ness\, n.
   The quality or state of being rash.
   [1913 Webster]

         We offend . . . by rashness, which is an affirming or
         denying, before we have sufficiently informed
         ourselves.                               --South.
   [1913 Webster]

   Syn: Temerity; foolhardiness; precipitancy; precipitation;
        hastiness; indiscretion; heedlessness; inconsideration;
        carelessness. See Temerity.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rashness
    n 1: the trait of acting rashly and without prudence [syn:
         heedlessness, mindlessness, rashness]
    2: the trait of giving little thought to danger [syn:
       recklessness, foolhardiness, rashness]