1550s, originally in a West Indian context, from Spanish canoa, a term 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 c.1600.
1842, from canoe (n.). Related: Canoed; canoing.
To deal with one's own problems, advancement, etc: My Dad kicked me out and told me to paddle my own canoe (1828+)