The "Happy!" file for her birthday gives a few lines of:

Where she, who stems the wound that bleeds,
A heroe's life may save:
And heroes saved, exulting, tell
How well her voice they knew:
How sorrow near it could not dwell,
But spread its wings and flew!
"Florence Nightingale" By Francis Bennock, Library of Congress, America Singing: Nineteenth-Century Song Sheets (but it seems unlikely this ever went into tradition.)

See the American Memory pages for the rest.