As others have said, the UK has an 'open border' agreement with the Republic of Ireland, meaning that UK & Irish citizens don't need any documentation to move between the two countries (as far as immigration rules are concerned).
All airlines require some form of ID, with the rules varying between airlines. (Ryanair is the only airline which only accepts passports).
However I note that travel will be by ferry. Again, each carrier is free to make their own rules.
Irish Ferries accept these:
Passport
Driving Licence
European Union identity card
Bank cards
Photo ID
Birth Certificate
This from the StenaLine website:
"British or Irish citizens travelling on our Irish Sea routes do not need a passport to travel to Britain or Ireland but are advised to take a form of identity. A driving licence, citizenship card or utility bill will usually suffice. A birth certificate will provide adequate proof of identity for your child to travel on our sailing".
From P&O:
"A Photo ID is only required on the Dublin/Liverpool route and is required for the driver of the vehicle ONLY. No form of ID is required for the car passengers".
Chris