The Pet Travel Scheme (PETS) allows cats and dogs to travel within participating countries without the need for quarantine. The scheme is outlined here:
Important note: Although the pet may now leave the UK to visit qualifying countries, he/she may not return to the UK (without quarantine) unless 6 months have passed from the date that the blood sample was taken. Therefore clients must be well-organised and allow at least 8 months before the proposed date of travel. It is essential that rabies boosters are kept up to date.
Further information about the PETS scheme is available from the DEFRA website:http://www.defra.gov.uk/animalh/quarantine/pets/