Brothers to John Kearney

I am the granddaughter of John Kearney who left Ireland for Australia.  The earliest Australian record I can find for him is a employment record for 1911.  His birth record is a Civil record Registration No 11802866  Line 426 born 2 Nov 1887 Super. Reg. Dist. Kanturk  Birth Registered at Milford  Registrar W P O'Leary Co Cork by his mother Mary Kearney formerly Nunan x her mark. see below.  His daughter in law, Margaret, living,  recalls John saying he had two brothers who both Immigrated.  One to South Africa and one to America.  It is his brothers information I am hope full of finding.  His parents were John Kearney and Mary Nunan married in the Roman Catholic Church Mildord on 19 February 1887  see below with more details. John's father, John, died in 1897, record below.  Over the last 10 years I have searched  any Census records I could find, Roots Ireland, Ancestry, Family Search, contacted Mallow History Centre, Irish genealogy and Find my Past and My Heritage without any luck. I was unable to find any Census records after his father's death and Mary may have gone to live with family and I could not find a positive record to confirm this. The barrier I find is that I am unsure of the Parish Name and hope you can help.  My aim is to find his brothers names and using our dna on line to find any American cousins. My public on line tree is OlsenfromNicholas on Ancestry and My Heritage. My name is Kim Lang and my email address is klbfd877@gmail.com      John came to Australia to his cousin Catherine Kearney (born 1868 registered in Milford)  who married in Australia to John Joseph Kerrigan and I grew up with Kerrigan Cousins in New South Wales.  https://www.ancestry.com.au/family-tree/tree/58310200/family?cfpid=402030012608.  Thank you very much for looking into this, with appreciation,  Kim .   PS  If I had his brothers names and the name of the Parish would I be able to write to them for more details?