Brewer's Dictionary of Phrase and Fable/Doff
Appearance
Doff is do-off, as "Doff your hat." So Don is do-on, as "Don your clothes." Dup is do-up, as "Dup the door" (q.v.).
"Doff thy harness, youth,
And tempt not yet the brushes of the war."
Shakespeare: Troilus and Cressida, v. 3.