I can only see 3 births for an Ann(e) Kearney in Co Down around May 1919. The most probable seems to be in Apr ? Jun 1919 registered in Newry, Vol 1, page 706; the other 2 were both registered in Belfast (part of which is in Co Down). Apr ? Jun 1919 Vol 1, page 369 & Apr ? Jun 1919 Vol 1, page 311.
You might need to order all 3 to see if any of them is the right one.
I looked for marriages in Co Down around that time. Closest I could find was Edward Kearney who married Mary McEvoy in Banbridge Apr ? Jun 1919, Vol 1, page 263. But you?ll need to order the birth certs before you can decide whether the marriage might be right.
You can order a photocopy of any of those certs from GRO Roscommon for ?4 per certificate. Put the place, year, quarter (where there is one), volume & page number on the application form (anywhere). Don?t worry about leaving some boxes blank. You don?t need to fill them all in if you have the reference details. http://www.groireland.ie/ You have to post or fax the form to them but they will e-mail the copy certificate to you if you wish. Tick the relevant box on the form.