The Collaborative International Dictionary of English v.0.48:

Whippersnapper \Whip"per*snap`per\, n.
   A diminutive, insignificant, or presumptuous person.
   [Colloq.] "Little whippersnappers like you." --T. Hughes.
   [1913 Webster]

WordNet (r) 3.0 (2006):

whippersnapper
    n 1: someone who is unimportant but cheeky and presumptuous
         [syn: whippersnapper, jackanapes, lightweight]

Moby Thesaurus II by Grady Ward, 1.0:

63 Moby Thesaurus words for "whippersnapper":
   JD, a nobody, a nothing, boldface, brat, brazenface, chutzpanik,
   cipher, common man, dummy, elf, enfant terrible, figurehead, gamin,
   holy terror, hussy, imp, insignificancy, jackstraw,
   juvenile delinquent, lightweight, little fellow, little guy,
   little monkey, malapert, man of straw, mediocrity, minx, nebbish,
   nobody, nobody one knows, nonentity, nothing, nullity, obscurity,
   pip-squeak, puck, punk, punk kid, pup, puppy, runt, saucebox,
   scrub, shrimp, small fry, small potato, small potatoes,
   smart aleck, smart-ass, smarty, smarty-pants, spoiled brat, squirt,
   squit, swaggerer, upstart, urchin, whiffet, wise guy, wise-ass,
   zero, zilch