The Collaborative International Dictionary of English v.0.48:

Childishness \Child"ish*ness\, n.
   The state or quality of being childish; simplicity;
   harmlessness; weakness of intellect.
   [1913 Webster]

WordNet (r) 3.0 (2006):

childishness
    n 1: a property characteristic of a child [syn: childishness,
         puerility]

Moby Thesaurus II by Grady Ward, 1.0:

47 Moby Thesaurus words for "childishness":
   anility, babyishness, boylikeness, caducity, callowness,
   childlikeness, decline, dotage, dotardism, girlishness, immaturity,
   imprudence, inadvisability, inattention, inconsideration,
   indiscreetness, indiscretion, inexpedience, infantilism,
   injudiciousness, irrationality, maidenliness, pompousness,
   puerilism, puerility, reasonlessness, recklessness,
   second childhood, senectitude, senile debility, senile dementia,
   senile psychosis, senile weakness, senilism, senility,
   senselessness, stuffiness, thoughtlessness, unintelligence,
   unreason, unreasonableness, unsensibleness, unsoundness,
   unthoughtfulness, unwisdom, unwiseness, witlessness



Bouvier's Law Dictionary, Revised 6th Ed (1856):

CHILDISHNESS. Weakness of intellect, such as that of a child.
     2. When the childishness is so great that a man has lost his memory, or
is incapable to plan a proper disposition of his property, he is unable to
make a will. Swinb. part. 11, Sec. 1; 6 Co. 23. See 9 Conn. 102; 9 Phil. R.
57.