I didn't find any promising leads for your Jane here in Ireland based on the details you mentioned, which is how I stayed into English census returns to see if there were clues I could use from these, e.g. a more detailed place of birth, or a possible Irish relation in the same household .. so was wondering about the place of birth references. English Marriage certs, same as Irish ones, usually include current place of residence, rather than place of birth - is the record you have that mentions Cork a copy of a church record ? p.s. what denomination church was Jane's marriage ?
There are about 70 matches for a birth of a Jane Quin/Quinn on the Irish BMD Index between 1864 and 1868, many of these with Jane as a middle name, and only one that I can see listed in any of the 20 or so registration districts which cover parts of Co, Cork and that's an 1866 birth in Lismore Registration district which although based in Co. Waterford covers a small part of Co. Cork. An Extracted Civil birth on FamilySearch rules this one out unfortunately as it shows that the father's first-name was Jerry.
If Jane's age on the census returns is slightly out and she was born before the start of civil records in 1864 then a search for parish records would be required. You can search Catholic Parish registers for the south west of Co. Cork on the IrishGenealogy website, but nothing promising there for a Jane in West Co. Cork during the mid 1860s, or Quinn baptisms with father's name Richard/Ricardo (he could be recorded in Catholic registers in Latin), records for parts of north and east Co. Cork (both RC and CofI) are available as transcripts on RootsIreland (pay-website) and although nothing with father's initial 'R' is showing up under a search of Cork records, there are some matches by father's initial in Co. Waterford, unfortunately no sign of any named Jane..though.. I wonder if your Jane went by a middle name later in life, but was registered and/or baptised under another name ? this could make a search difficult as middle names are often not included in birth or baptism records.
Only other possible lead I can think of at the moment is that sister you mentioned - do you remember anything about her ?
p.s. have you located your Jane on the English 1881 census ?
