Coming to Cork but not sure where to go

I would suggest starting the search with baptisms for Catherine and Julia, using their approximate dates plus parents names to try and narrow down the location - i.e. parish. If some details can be found then you should at least know which parish they lived and possibly also the name of the townland.

Very few Roman Catholic parishes include details of death/burials, so probably best to focus on baptisms and or marriages.

Records for most of the Catholic parishes in South West Co. Cork are included on the free Irish Genealogy Website, and details for parishes for many of the parishes in North and East Co. Cork are on the RootsIreland pay-website.

The best lead I've seen so far is on the RootsIreland index, and and is a Catherine Walsh baptised during 1847 in Blarney Catholic parish, which is based in the town of the same name. Parent names are matching Edmond & Ellen, and mother's maiden surname Nugent.

The transcript on RootsIreland can be viewed for a small fee and should usually show names of two godparents. The record may mention a place of residence for the family within the parish, often the name of a townland.

Not certain if this is your Edmond, but worth noting, since the location matches... there's listing for an Edmond Walsh on Griffith's valuation, which is dated October 1852 for this area. He is listed with about 15 acres of Land at the townland of Dawstown, in Garrycloyne civil parish (which includes the town of Blarney). The listing doesn't mention a house, so maybe he lived elsewhere..

The details of Griffith's Valuation are available on the AskAboutIreland website, and include transcripts, images of the records and maps.