I located John's baptismal record on the free Irish government site www.irishgenealogy.ie He was baptized June 30 1862 in Duagh RC church. Also found baptismal records for three siblings but did not see the marriage record for the parents and maybe the marriage was in a parish other than Duagh. The other cchiildren were Tom October 21 1857 Joan March 27 1860 Mary December 16 1864. I looked for a civil birth record for Mary (civil registration started in 1864) but did not locate a record. Nor all births were registered particularly in the early years of the process.
I looked for civil death records for Thomas and Kate with no success and also did not see any of the family in the Duagh area in the 1901 census. All of the Doody families in the Duagh are were in Knockavallig townland so possibly your family was also from there.
Let me know if you have any questions.