Here's a version that's actually attributed to an author, from:

Dodge, Mary Mapes. St. Nicholas. New York, N.Y.: The Century Co., 1890, Volume 18, page 401:

ALPHABET SONG
Emma C. Dowd.

A, B, C, D, E, F, G,—
Baby and I will sail the sea;
H, I, J, K, L, M, N,—
Across the ocean and back again;
O, P, Q, R, S, T, U,—
Now on the railway, choo, choo, choo!
V and W, X, Y, Z,—
Home is the best place for baby and me.