As Lonecat said, if you're sailing direct from the UK to N Ireland you don't need a passport, but if you're setting food in The Republic of Ireland you do.
It's ridiculous, as there are no border controls or checks at the ferry ports, let alone border crossings within Ireland itself, but they have threatened spot checks and if your dog isn't fully passported you run the risk of them being impounded at your cost until they meet the requirement and are allowed to travel.
We travel to Southern Ireland regularly and know lots of people that haven't bothered sorting passports for their dogs to do similar journeys, but personally, I don't think it's worth the risk, especially as they are cracking down more these days due to the number of rescue dogs being brought in in private vehicles to try and circumvent the Balai Directive.
Basically, if you'd like to visit The Republic of Ireland, you just need to make sure your dog is up to date with their vaccinations and fully vaccinated against Rabies at least 21 days prior to travel and get your vet to fill in, stamp and sign the passport and do the accompanying paperwork. You don't need to do anything about tapeworm treatment, as both countries are exempt anyway (although the info on the Irish Ministry of Agriculture website is confusing in relation to this).
The initial cost of the passport can seem a bit expensive at first, but the vets have an awful lot of admin to do to comply with border control law etc, so the lion's share of their work is actually done outside of the consultation for the Rabies vaccination and passport stamps. After that it's just, iirc, a three year booster to keep it up to date.