" ... Annie born (Hert) ... "
Are there any legibility issues around this or is it an unequivocal interpretation from the death certificate that her maiden surname is Hert? Hert is really not common at all in Ireland, nor Hurt, though Hart is a good bit more common. But even for Hart, nothing is jumping out.
If you hadn't provided Annie's surname, a candidate would have been a Robert McAleese who married Anne Loughan in Antrim High Street Presbyterian Church in 1857 (I think they had a son George, couldn't see a Thomas, but online church records are patchy). But it's a great leap from Hert to Loughan!
As informant's information on death certificates is notoriously unreliable, there's a bit of me thinking that you might want to try and corroborate Annie's previous and/or birth surnames, I could be wrong but I'm just a little bit suspicious of the "Hert".