Hi Leandra,
I have stuff to send you on Doodys, but Family Search now includes Irish b, m & d records prior to civil registration. This is new. I had a look and couldn't find the birth or marriage details of Andrew & Bridget. However, as they married in Feb 1861 and had first children in Aug 1863, there is a good chance that those were their first. Shipping records of their emigration should confirm.
Speak soon.