
As we know, up until recently there was no need for animals to be rabies vaccinated or have a passport to travel between the UK and Ireland. That changed in January 2012 when the passport titre test requirement was dropped and animals could travel into the UK from Europe 3 weeks after vaccination; at this time the legal situation changed and Ireland (being a separate EU country) was included in the scheme. In practice this meant nothing - passports were never (and as far as I know are never) checked in either Ireland or the UK and many people never bothered to get one.
Today local Trading Standards siezed a cat that had come from ireland without a passport. in law it had been illegally imported, and the owners were given the choice of quarantining it or euthanasing it: they chose euthanasia.
It might be sensible, therefore, if you're planning to travel to Ireland with your dog to consider the journey in the same way as you would a trip to mainland Europe, and get a passport. It might never ever be checked - but at least you wouldn't be put in this situation.