(Anglo-Saxon slaepen). Crabbe's etymology of doze under this word is exquisite:
“Doze, a variation from the French dors and the Latin dormio (to sleep), which was anciently dermio and comes from the Greek derma (a skin), because people lay on skins when they slept ”! —Synonyms.
To sleep away. To pass away in sleep, to consume in sleeping; as, to sleep one's life away. To sleep off. To get rid of by sleep
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894