When travelling with your pet to a show outside the EU, you should work out the conditions for the export with for example the organiser of the show. Note, that the conditions for export are often exactly the same as for other pet exports.
When travelling to a show it is important to note how many pets can travel with one person to the country of destination and back to Finland. The numbers may vary. The minimum age of pets returning to Finland is 6 months and more than 5 pets can be transferred, whereas the country of destination (the country where the show is organised) may adhere to stricter regulations. Be prepared to show proof of participation in a show in conjunction with the border-crossing formalities.
Also note that you have to be able to prove that the pets travelling with you in and out of the country are the same, otherwise the interpretation may be that you have sold or acquired a new pet during your trip.