According to "Early Years In The United States: New York", there was little information about J. C. Mueller and Louise Schirmer and their life or years in the State of New York other than family legend.
However, once I located J. C. Mueller's immigration information placing him in New Hampshire in 1869 and naturalizing in New York City in 1873, I noted his naturalization paperwork placed him in Coxsackie as a farmer. So while the evidence that we have is circumstantial, it's more likely than not that the family legend is mostly correct.
Age at Marriage
John was 25 years and 2 months old; Louisa was 23 years old. (They were married 22 years and 1 month).
Family legend has both John Carl and Louisa arriving (separately) in 1867, and being married in 1872. No supporting documentation has ever been found.
In September 2009, I located his 1889 passport application that verified his immigration information. He traveled on the Westphalia from Hamburg.
In the passport application, John says he immigrated on or about 28 Aug 1867. The Westphalia wasn't launched until 1868. There is a passenger listing on the maiden voyage arriving 28 Sep 1868 for Johann Müller, age 22. I think that's the right person.
Residence
13 Aug 1869
Manchester, Hillsborough County, New Hampshire, USA
Passport Application for John Charles Mueller J. C. Mueller took a trip outside the US some time after June 1889. Because he was a naturalized citizen, his passport application gave invaluable information about his immigration.
[S296] Passport Application for Mueller, John Charles.
[S322] Declaration of Intent to Immigrate; Mueller, John Carl.
The State of New Hampshire
TO THE HONORABLE JUSTICES OF THE Superior Judicial Court
holden at Manchester in and for the County of Hillsborough, on the first Tuesday of June A. D. 1869
RESEPECTFULLY REPRESENTS John Charles Mueller
of Manchester in said County, that
he is a free white person, and an alien of Louis Third Archduke of Hessian in Germany
and that he has resided in the United States for two years last past, and
he hereby declares that it is bona fide his intention to become a citizen of the United States of
America, and to renounce all allegiance and fidelity to every foreign Prince, Potentate, State
and Sovereignty whatsoever, and particularly to Louis Third
whose subject he has heretofore been. He, therefore, prays that his Declaration and In-
tention may become a record of this Honorable Court, agreeably to the laws is such case made
and provided.
(signed) John Charles Mueller
[S459] Austin, Texas, City Directory, 1885, (Morrison & Fourmy).
[S461] Austin, Texas, City Directory, 1887, (Morrison & Fourmy).
[S460] Austin, Texas, City Directory, 1889, (Morrison & Fourmy).