The Collaborative International Dictionary of English v.0.48:

Speediness \Speed"i*ness\, n.
   The quality or state of being speedy.
   [1913 Webster]

WordNet (r) 3.0 (2006):

speediness
    n 1: a rate that is rapid [syn: celerity, quickness,
         rapidity, rapidness, speediness]

Moby Thesaurus II by Grady Ward, 1.0:

45 Moby Thesaurus words for "speediness":
   agility, air speed, alacrity, briskness, celerity, decisiveness,
   dispatch, expedition, expeditiousness, fastness, flight, flit,
   flurry, ground speed, haste, hurry, hustle, immediacy,
   immediateness, instantaneousness, knots, lightning speed,
   miles per hour, nimbleness, precipitation, promptitude, promptness,
   punctuality, punctualness, quickness, rapidity, readiness,
   round pace, rpm, rush, rustle, sharpness, smartness, snappiness,
   speed, spryness, summariness, swift rate, swiftness, velocity