The EU's food safety strategy:

Imported or homegrown, food must meet high EU standards.
The EU-wide food strategy has 3 core elements:
Plus special measures where specific consumer protection is justified:
The EU takes great care to ensure that traditional foods are not forced off the market by its food standards, that innovation is not stifled, and that quality does not suffer.
When new members join the EU (and hence the single market), transitional measures may be needed to allow them time to catch up with the EU's high food safety standards. But in the meantime, they may not export foodstuffs that do not meet those standards.
For GMOs, cloning and nanotechnology – collectively known as novel foods – the Commission follows the path of responsible innovation that gives EU citizens the best guarantee of safety and the strongest impetus for economic growth.

He can have his own passport and travel with you.
Animals can also be moved freely throughout the EU. But the health and welfare standards that apply on the farm must also be met during transport. When there are outbreaks of animal diseases, the EU steps in quickly if necessary to freeze trade.
EU 'pet passports' enable people to take their pets with them when they travel. However, to prevent diseases spreading, precautions apply to pets just as they do to other animals.
All plants and plant material can be moved throughout the EU, as long as they are pest-free. Screening of imported plant material and monitoring of EU territory help detect new pests at an early stage.
This allows preventive action to be taken, which helps avoid curative measures such as the use of pesticides. A plant passport attached to a young tree indicates that it was grown under healthy conditions.
The EU operates an early warning system to protect people from food poisoning. This system also spots whether foodstuffs contain banned substances or excessive amounts of high-risk substances, such as residues of veterinary medicines in meat or carcinogenic colourings in food.
When a threat is spotted, alerts go out across the EU. Stopping a single batch may be all that is needed, but, if necessary, all shipments of a particular product from a farm, factory or port of entry will be stopped. Products already in warehouses and shops may be recalled.
Whenever there are significant outbreaks of animal disease or food poisoning affecting European consumers, EU authorities can trace the movement of food products all the way back up the production chain – whether live animals, animal-based products or plants.
These traceability and risk management functions are provided by TRACES (Trade Control and Expert System), an electronic system of border controls and certification for traded goods.
Science is the essential foundation on which the EU bases decisions on food. The European Food Safety Authority (EFSA) provides advice when legislation is being drafted and when policymakers are dealing with a food safety scare.
The Commission applies the precautionary principle: it will act without delay if the scientists say there is even a potential danger.
The Commission enforces EU feed and food law by checking that EU legislation has been properly incorporated into national law and implemented by all EU countries, and through on-the-spot inspections within and outside the EU.
The Commission’s Food & Veterinary Office (FVO) checks individual food production plants, but its main task is to verify that EU and non-EU governments have the necessary mechanisms in place to ensure that their own food producers comply with the EU’s high food-safety standards. Since 2013, the scope of the FVO's activities has been extended to include medical devices.