We usually trevel with P&O ferries from Cairnryan, Troon to Larne, then travel down there's ferries from Liverpool to Dublin also. There's a few companies, P&o being one, Irish Sea, Stenna, depending on where your travelling from, Belfast/Larne is about 2hours drive to Dublin.
Yes, unfortunately the dogs stay in the vechicle, but ours don't even notice, they lie and sleep, always leave the windows open a bit, can get warm in the car deck. We tried to get discout from the IKE, when we were over at the circuit, but they dont dont it know!