The University of North Carolina has a copy of Hans Georg Nägeli, Life Let Us Cherish. With variations by Mozart. published in New York by W. Dubois in 1818. Several copies attributed to Mozart in the Levy collection at Johns Hopkins.
The best playing music is on the ABC Notation website ... it's in G instead of F, and there are several websites that will transpose it down to "D for dulcimer."
Nancy Cleaveland has the best background on the song at her Pioneer Girl: Fact and Fiction in Laura Ingalls Wilder website:
"Life Let Us Cherish" was originally a song entitled "Freut Euch des Lebens," written in 1796 by Swiss poet Johann Martin Usteri and composer Hans Georg Nageli. It became immensely popular in America as "Life Let Us Cherish." ...With lyrics and a MIDI file. Cleaveland has a lot of period music in her INDEX OF SONGS FROM THE "LITTLE HOUSE"® BOOKS.
"Freut euch des Lebens" by German pop singer Edith Prock
The Dictionary of Music and Musicians on Wikisource has this: "LIFE LET US CHERISH. A favourite German song, commencing 'Freut euch des Lebens,' the author of which is Martin Usteri of Zurich ; first published in the ' Gottinger Musen- almanach ' for 1 796 without the author's name. The music was written in 1793 by Hans Georg Nageli. It is used as subject for the elaborate variations which form the last movement of Woelfl's celebrated sonata called ' Non plus ultra.' [R.M.]"