EU rules make it easy to travel to another EU country. With a few exceptions, pets can travel with you to another EU country or from a non-EU country to an EU country if it has:

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• been micro-chipped (in line with the technical requirements of Annex II of the EU Regulation on the movement of pets) or has a clearly readable tattoo if applied before 3 July 2011

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• been vaccinated against rabies

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• a valid European pet passport, when travelling from an EU country or Northern Ireland to another EU country or Northern Ireland or an EU animal health certificate, when travelling from a non-EU country.

 

 For entry to some countries (Finland, Ireland, Malta, Norway, Great Britain and Northern Ireland) dogs must also have a treatment against the tapeworm Echinococcus multilocularis. You do not need to treat your dog for tapeworm if you’re going directly to Great Britain from Finland, Ireland, Northern Ireland, Malta or Norway. This must be done at least 24 hours and no more than 120 before entering the country. 

There is a lot of helpful information here.