From: www.disabilityrightsuk.org/news/2018/august/how-prepare-if-uk-leaves-eu-no-deal
Pet travel - guide and assistance dogs
Scenarios vary according how the EU classifies the UK.
The UK becomes a ‘third country’, linked to a country’s animal health status. It could have one of three catgorisations: Part 1 listed, Part 2 listed or ‘unlisted’. On arrival in the EU, pet owners travelling with their pet would still be required to report to a Travellers’ Point of Entry.
Part 1: Changes needed to documentation but no change for pet owners from what they currently need to do in terms of health preparations.
Part 2: Before a dog could travel from the UK to an EU country for the first time, it would need to be taken to an Official Veterinarian (OV) at least 21 days in advance to ensure the dog has a microchip and rabies vaccination. The OV would issue a health certificate. This would be valid for ten days after the date of issue for entry into the EU, and for four months of onward travel within the EU. Health certificates would have to be issued for each trip to the EU.
Unlisted: You would need to discuss preparations for your dog’s travel with an Official Veterinarian (OV) at least four months in advance of the date you wish to travel. You would need to prove your dog is effectively vaccinated against rabies. If your dog has never had a vaccination or it is not up to date you will need to have a blood test 30 days after the vaccination followed by a further three-month waiting period before you can travel with your dog.