Douay, Parish of Mevagh

People tended to give their townland, so I'd suspect Douay is a mis-spelling of a townland in Mevagh. Possibly Doagh which has several Shiels/Sheals in it in the 1901 census. I would try to get a copy of Bridget's birth certificate to confirm the information you have. Mevagh is in Millford Civil Registration district. There were two Bridget Shiels births there in 1872. Volume 7, page 307 and Volume 12, page 268. I'd start with the volume 12 birth which seems likely to be later in the year. Let me know if you don't know how to order an Irish birth certificate and I'll explain.

There are several version of an extracted civil birth record that fit - one shows location as 'Rossguill' - see here

Rosguill is a registration sub-district within Millford district, and includes Mevagh civil parish mentioned above. So I'd go along with Doagh townland.

edit : probable younger sibling to your Bridget, a Catherine Sheils, born 1st November 1876, same registration district - see here (FamilySearch Extracted civil births)

Thank you both for your comments and offers of help. I actually live in France but have already obtained a copy of her Birth Certificate from Ireland and on closer inspection of the certificate I can see that the Registrar, a David Christie, writes his n's looking like u's! I am now pretty convinced that this is the place as my mother used to tell me her mother, Bridget, had once got into difficulties in the inlet when she was little and the family dog helped her to get out. I had great difficulty originally tracing Bridget in Scotland until I discovered she had changed her birth name of Bridget to Bedelia (the "Anglicised" version which appears on all her subsequent records e.g. Marriage cert, Death Cert, Childrens' Birth Certificates etc.

Also shanew147 for the info. on Catherine as I have no knowledge of other family members but I will now try to follow these excellent leads you have both given me. Many thanks indeed.