On a pedantic note, only UK and Irish documents are accepted this way, which means it needs to be a driving licence. Assuming it is, you won’t have any issue flying BA. On arrival at DUB make sure you go to a manned booth as it won’t work in the e-gates, and as above it does make it quicker to proactively offer your BP to the officer, so it would be worth getting a paper one on departure. That’s more useful than a birth certificate.