one of the familysearch trees mentioned above in reply #6 says Patrick was born 1 February 1825, in Hospital, Limerick
https://www.familysearch.org/tree/person/details/LBPV-76Jhere is his baptism:
Hospital Parish, Limerick, Baptisms
20 February 1825, Patrick son of John Kirby and Hanora Riordan, sponsors: James Kirby and Anne Riordan
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the same tree says that John & Hanora had a son named Simon born April 1831. Simon is an unusual name. Joseph named one of his sons Simon, according to (maybe) a different tree.
Simon's baptism:
19 April 1831, Simon, son of John Kirby and Hanora Riordan. sponsors: Daniel Riordan and Anastasia McNamara
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from Reply #7, on the 1900 Census Daniel Riordan Kirby says he was born in May 1826
here is his baptism:
28 May 1826, Daniel, son of John Kirby and Hanora Riordan, sponsors: Patrick Riordan and Catherine Gibbons
all the baptisms are found at
https://registers.nli.ie/parishes/0268---------
So you have 3 brothers from Limerick in the same county in the US. The evidence is pretty strong for Joseph Kirby of Utica Township, Iowa, being the one baptized 13 Jan 1836 in Hospital, Limerick, not the man who died in Victoria, Australia, in 1907. At the very least, you definitely can't rule him out.
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By the way, for county histories, I only found:
only an Agnes Kirby mentioned in HISTORY OF Chickasaw and Howard Counties IOWA.
BY W. E. ALEXANDER.
DECORAH, IOWA. WESTERN PUBLISHING COMPANY.
1883.
at
http://iagenweb.org/howard/history/1883%20Howard%20Co%20Biographical%20Sketches.htmand a Dan Kirby is mentioned in HISTORICAL AND REMINISCENCES OF CHICKASAW COUNTY,IOWA.
BY J. H. POWERS
DES MOINES: IOWA PRINTING COMPANY, 1894.
at
http://iagenweb.org/chickasaw/history/historypowers1894.htm