This is the latest advice in the event of a no-deal Brexit from the Government.
https://www.gov.uk/guidance/pet-travel-to-europe-after-brexit
The advice sets out that pet owners intending to travel with their pet from the UK to EU member states would need to visit their vet at least four months in advance of their travel date. This means that those wishing to travel to the EU on 1 November 2019 would need to discuss requirements with their vet before the end of June.
If the UK is classed by the EU as an unlisted third country for pet travel, vets would have to carry out a blood titre test to prove that pets have a sufficient rabies antibody level to meet EU requirements. Depending on a pets’ history, and the result of the test, the process could take at least four months.
In a no deal scenario, EU pet passports issued by UK OVs would no longer be valid. Instead, a pet travelling from the UK to the EU would need an Animal Health Certificate (AHC).
We will update you as and when we get more information.