The Levy Collection has this sheet music (Click here).

Title: Gideon's Band. Song and Chorus.
Composer, Lyricist, Arranger: Music Arranged By Chas. R. Dodworth.
Publication: Philadelphia: Lee & Walker, 722 Chesnut St., 1861.
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: Oh! Keep your hat upon your head, Oh, keep your hat upon your head
First Line of Chorus: If you belong to Gideon's Band, Oh, here's my heart and here's my hand
Performer: Sung With Immense Applause in the Musical Extravaganza of Mazeppa at Mrs. John Drew's Arch St. Theatre. Also by the Buckley's Serenaders.
Engraver, Lithographer, Artist: T. Sinclair's Lith. Phila.
Subject: Portraits
Subject: Caricatures
Subject: Musicians
Call No.: Box: 052 Item: 008

The music may have been popular, because at least three songs to the tune of "Gideon's Band" ["M'Clellan's band," "We'll be free in our Maryland," and "If you belong to Dixie's land"] are in the America Memory collection.

~Masato