The title is "I'm On My Way to Dublin Bay." You can hear it here.

The Levy Collection has its sheet music. Click on the title below.

Title: I'm On My Way To Dublin Bay. Song.
Composer, Lyricist, Arranger: Lyric and Music by Stanley Murphy.
Publication: New York: Jerome H. Remick & Co., 1915.
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: Michael Shea he marched away with the Dublin Fusiliers
First Line of Chorus: Good-bye! I'm on my way to dear old Dublin Bay