"light boat propelled by hand-held paddle or paddles," 1550s, originally in a West Indian context, from Spanish canoa, a word used by Columbus, from Arawakan (Haiti) canaoua. Extended to rough-made or dugout boats generally. Early variants in English included cano, canow, canoa, etc., before spelling settled down 18c. To paddle one's (own) canoe "do for oneself make one's way by one's own exertions," is from 1828, American English.
THEY have a very expressive term at the West, in speaking of a man who would be the architect of his own fortune, that he must paddle his own canoe. [Harper's New Monthly Magazine, May 1854]