The Collaborative International Dictionary of English v.0.48:

Quickness \Quick"ness\, n.
   1. The condition or quality of being quick or living; life.
      [Obs.]
      [1913 Webster]

            Touch it with thy celestial quickness. --Herbert.
      [1913 Webster]

   2. Activity; briskness; especially, rapidity of motion;
      speed; celerity; as, quickness of wit.
      [1913 Webster]

            This deed . . . must send thee hence
            With fiery quickness.                 --Shak.
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            His mind had, indeed, great quickness and vigor. --
                                                  Macaulay.
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   3. Acuteness of perception; keen sensibility.
      [1913 Webster]

            Would not quickness of sensation be an inconvenience
            to an animal that must lie still ?    --Locke
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   4. Sharpness; pungency of taste. --Mortimer.
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   Syn: Velocity; celerity; rapidity; speed; haste; expedition;
        promptness; dispatch; swiftness; nimbleness; fleetness;
        agility; briskness; liveliness; readiness; sagacity;
        shrewdness; shrewdness; sharpness; keenness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

quickness
    n 1: skillful performance or ability without difficulty; "his
         quick adeptness was a product of good design"; "he was
         famous for his facility as an archer" [syn: adeptness,
         adroitness, deftness, facility, quickness]
    2: intelligence as revealed by an ability to give correct
       responses without delay [syn: mental quickness,
       quickness, quick-wittedness]
    3: a rate that is rapid [syn: celerity, quickness,
       rapidity, rapidness, speediness]

Moby Thesaurus II by Grady Ward, 1.0:

195 Moby Thesaurus words for "quickness":
   ability, abruptness, acuity, acuteness, address, adeptness,
   adroitness, agility, air speed, airmanship, alacrity, alertness,
   animation, anxiety, anxiousness, appetite, aptitude, aptness,
   artfulness, artisanship, artistry, attention, attentiveness,
   avidity, avidness, bat, braininess, bravura, breathless impatience,
   brightness, brilliance, briskness, capability, capacity, celerity,
   cheerful readiness, clear thinking, cleverness, command,
   competence, control, coordination, craft, craftsmanship, cunning,
   decisiveness, deftness, dexterity, dexterousness, dextrousness,
   diplomacy, dispatch, docility, eagerness, educability, efficiency,
   elan, esprit, expedition, expeditiousness, expertise, facility,
   fastness, feverishness, finesse, flair, flight, flit, flurry,
   forwardness, furiousness, gait, genius, giftedness, gifts, grace,
   grip, ground speed, gust, gusto, handiness, haste, hastiness,
   horsemanship, hurriedness, hurry, immediacy, immediateness,
   impatience, impetuosity, impetuousness, impressionability,
   impulsiveness, ingeniousness, ingenuity, instantaneousness,
   intelligence, keen desire, keen-wittedness, keenness, knots,
   know-how, life, lightning speed, liveliness, malleability,
   marksmanship, mastership, mastery, mental alertness,
   mercurial mind, miles per hour, moldability, motivation,
   native cleverness, nimble mind, nimble-wittedness, nimbleness,
   nous, overhastiness, pace, plasticity, pliability,
   practical ability, precipitance, precipitancy, precipitateness,
   precipitation, precipitousness, proficiency, promptitude,
   promptness, prowess, punctuality, punctualness, quick parts,
   quick thinking, quick wit, quick-wittedness, rapidity, rashness,
   readiness, ready wit, receptivity, recklessness, resource,
   resourcefulness, round pace, rpm, rush, savoir-faire, savvy,
   seamanship, sharp-wittedness, sharpness, skill, skillfulness,
   sleeplessness, smartness, smarts, snappiness, speed, speediness,
   spirit, sprightly wit, spryness, style, suddenness, summariness,
   susceptibility, swift rate, swiftness, tact, tactfulness, talent,
   teachability, teachableness, technical brilliance,
   technical mastery, technical skill, technique, timing,
   trainableness, velocity, verve, virtuosity, vitality, vivacity,
   wakefulness, willingness, wit, wizardry, workmanship, zest,
   zestfulness