Ó Dónaill gives the verb Tafainn as being transitive and meaning to hunt, pursue, drive off/out, chase away, expel and the noun Tafann as being the verbal noun of Tafainn and also the (act of) barking, bark.
O'Reilly (1864) on the other hand gives Tafanaim as I yelp, bay, bark, pursue, expel, rout.
Another verb for bark is amhastraigh which Ó Dónaill gives as being intransitive, so one could say Amhastraíonn an madra.
I mean, I've heard people saying this kind of thing tongue-in-cheek. "Better take the dog out, he's been shouting his head off for two hours."
But it's important to know whether this would be a similarly humorous, anthropomorphic turn of phrase in Irish, or just a straightforward way of saying the dog is barking.
Our family dog only barked a few times in succession as a pup. As an adult dog, he was practically silent. Sometimes a child would drop something on him and he would yelp, a different sound altogether. When he did bark, it was a single, loud, deliberate shout, a sort of doggy "Hey!" It was always an unusual exclamation, meant as an alert, rather than an idle, repetitive yelling, if you see what I'm saying.
From what dictionaries say, it seems like béic just means something along the lines of "to create a loud vocal sound", basically anything in dialogue where the author is trying to be fancy: bellow, exclaim, shriek, whatever. And while it doesn't mean the specific bark that a dog makes (that'd be amhastraigh), I'm don't know exactly if it's common to use it in this context, but I'm sure it would work fine.