Non-commercial movement of dogs, cats nad ferrets
EU rules on travelling with pets and other animals in the EU - Your Europe
Non-commercial movement of other pet animals in EU
There are no requirements or documentation for pet animals such as rabbits, hamsters, mice, rats, etc., unless the legislation of the EU country to which the animal is moved provide otherwise.
In the case of species of animals covered by the Washington Convention (CITES), they should be accompanied by appropriate documents. The authority responsible for providing information is the Ministry of the Climate and Environment.