I have just found the original in J.P. McCaskey's Franklin Square Song Collection: Two Hundred Favorite Songs and Hymns for Schools and Homes, Nursery and Fireside, No. 1 (New York: Harper & Brothers, 1881, p. 9). There's no mention of author/composer/source. Meter is 6/8, but is not indicated on the score.

X:2
T:The Golden Rule
M:6/8
L:1/8
B:J.P. McCaskey, Franklin Square Song Collection, No. 1 (1881, p. 9)
K:Bb
F|d2 d d2 B|cB G F2 F|B2 B Bc d|c3-c2 F|
w:The gol-en rule, the gold - en rule, Oh, that's the law_ for me;_ Were
w:Were this the rule, in har - mo-ny Our lives would pass_ a-way;_ And
d2 d d2B|cB G F2 F|B2 B AB c|B3-B2 B|
w:this the law for all_ the world, How hap-py we_ should be._ The
w:none would suf-fer, none _ be poor, And none their trust_ be-tray.
c2 c c2 c|d2 d d2 d|e2 d dc B|c3-c2 F|
w:gold-en rule, the gold-en rule, Oh, that's the law_ for me;_ To
d2 d d2 B|cB G F2 F|B2 B AB c|B3-B2|]
w:do to oth-ers as_ I would That they should do_ to me._