Parents of Timothy Harrington?

My gg grandfather was Timothy Harrington. I recently found his death certificate that indicates he was born in 1806.  All of Tim's documents indicate that he was born in Cork, Ireland.  I found a document that might be his baptismal certificate that gives the parents as John Harrington and Ellen Lane.  The Timothy Harrington in the document was baptized in Kinsale, Cork and Ross on 4 July 1806.  This would follow naming traditons as my g grandfather was John Timothy Harrington.  I also have a number of DNA matches for the Lane surname.

Here are more details on Tim.  He immigrated in about 1843 to New York City.  Married Margaret McDonald/McDonnell, I believe in NYC as she immigrated in about 1845 but I have not found marriage documents.  Their son John Timothy was born in Manhattan, New York in 1848.  Tim died in Manhattan, New York City, New York in 1877.  He is buried in Calvary Cemetery with his wife Marg, her sister Bridget, and a number of my g aunts, g uncles and cousins who died as children.

I am attaching the baptismal certificate I found on Find My Past.  Is there anyway to find out more about John and Ellen Lane Harrington?  Are there other children associated with them?

I am at a brick wall for Tim.

Thank you for any assistance you may be able to provide.

Rachel Knapik, Seattle, WA