c. 1300, "a pulling, act of imparting notion by towing," in various senses; verbal noun from draw (v.). The meaning "act of forming or tracing by a pen, pencil, etc." is from late 15c,; that of "picture or representation produced by drawing" is from 1660s.
Drawing-board, "board on which paper is stretched for use in drawing," is from 1725; used in figurative expressions, with the sense of "beginning, starting point" is by 1941 (in the Peter Arno "Well, back to the old drawing board" cartoon in the New Yorker).