The title of your question doesn't seem to match it's content. You appear to have moved Dublin into Northern Ireland! - That's a sure way to upset the Irish ;-)
You've not stated how you're travelling but it's unlikely that your child would need any form of photo-id. (Different carriers may have different rules). From the Ryanair website:
"Photo-Id for children under 16 years is not required in the following circumstances:
Children travelling with an adult on UK domestic flights and UK-Republic of Ireland-UK routes. . . "
http://www.ryanair.com/site/EN/faqs.php?sect=p id&quest=photoid
Chris