Source : Webster's Revised Unabridged Dictionary (1913)

Dozy \Doz"y\, a.
   Drowsy; inclined to doze; sleepy; sluggish; as, a dozy head.
   --Dryden.

Source : WordNet®

dozy
     adj : half asleep; "made drowsy by the long ride"; "it seemed a
           pity to disturb the drowsing (or dozing) professor"; "a
           tired dozy child"; "the nodding (or napping)
           grandmother in her rocking chair" [syn: {drowsy}, {drowsing(a)}]
     [also: {doziest}, {dozier}]