“Paddle your own canoe” was printed in American newspaper poetical verses in 1826, 1845, 1854, 1864 and 1866; some of the verses were sung. The New-York Mirror of May 23, 1840 defined “paddle your own canoe” as meaning the same as “mind your own business.” John Russell Bartlett’s Dictionary of Americanisms (1859) defined “paddle your own canoe” as a “figurative Western phrase, meaning to make one’s own way in life, to be the architect of one’s own fortunes.”
 
“Love many, trust few, and always paddle your own canoe” (also “Love towards many, trust in few, and always paddle your own canoe”) has been a popular verse used in autograph albums since at least 1879.
   
 
(Oxford English Dictionary)
to paddle one’s own canoe: to make one’s way by one’s own exertions, to be self-reliant; to look after one’s own interests.
1828 J. Hall Lett. from West 261 It seems that they were not so well skilled in navigation as the Lady of the Lake, who ‘paddled her own canoe’ very dexterously.
1854 S. T. Bolton Paddle Your Own Canoe (song) i, Where’er your lot may be, Paddle your own canoe.
 
15 July 1826, Pensacola Gazette and West Florida Advertiser (Pensacola, FL), pg. 1, col. 2:
For the Pensacola Gazette.
To B.
(...)
Hereafter, when you write, write well,
Let ev’ry line for something tell,
And show the world that you,
Without an Indian’s bushes can,
(Or schoolboy’s verse, of Gottengen,)
Paddle your own canoe!
 
Google Books
23 May 1840, The New-York Mirror (New York, NY), pg. 380, col. 1:
“Paddle your own canoe,” meaning, “mind your own business,” is another expressive sample of western phraseology, which, like that just commented on, it would seem has first been rendered poetical in Texas.
 
Chronicling America
20 December 1845, The Columbia Democrat (Bloomsburg, PA), pg. 4, col. 1:
PADDLE YOUR OWN CANOE.
My father died, God rest his soul,
When years I numbered two,
And left me ‘midst the world alone,
To paddle my own canoe.
 
Chronicling America
23 January 1854, London (TN) Free Press, pg. 1, col. 4:
PADDLE YOUR OWN CANOE.
The following has the spark of originality, and contains some good advice. It is from the pen of Mrs. SARAH T. BOLTON, of Indianapolis:
 
Voyager upon life’s sea,
To yourself be true,
And where’er your lot may be,
Paddle your own canoe.
 
Google Books
Dictionary of Americanisms:
A Glossary of Words and Phrases Usually Regarded as Peculiar to the United States
Second Edition
By John Russell Bartlett
Boston, MA: Little, Brown and Company
1859
Pg. 307:
TO PADDLE ONE’S OWN CANOE. A figurative Western phrase, meaning to make one’s own way in life, to be the architect of one’s own fortunes.
 
Chronicling America
13 July 1864, The Weekly Perrysburg Journal (Perrysburg, OH), pg. 1, col. 4:
PADDLE YOUR OWN CANOE.
UP this world, and down this world,
And over this world and through,
Though drifted about,
And tossed without,
Why, paddle your own canoe.
 
Chronicling America
10 August 1866, The Lincoln County Herald (Troy, Lincoln County, MO), pg. 2, col. 4:
Mind Your Own Business.
All have their several tasks in life,
Let each his own pursue;
Don’t touch the tiller of my boat;
Paddle your own canoe.
   
Google Books
Selections for Autograph and Writing Albums
New York, NY: Charles A. Lilley, Publisher
1879
Pg. 92:
Love many, trust few,
And always paddle your own canoe.
 
Chronicling America
15 January 1885, The National Tribune (Washington, DC), pg. 7, col. 2:
Here is an album verse from a girl (13), living in the quiet village of Algonquin, Ill.:
 
Love many; trust few;
And always paddle your own canoe.
 
29 July 1886, The Rockingham Register (Harrisonburg, VA), pg. 3, col. 5:
On a blank leaf of a well worn copy of the New Testament, he read this good advice, which he copies for the young men of his acquaintance in Rockingham:
 
“Love towards many, trust in few,
And always paddle your own canoe.”