[CFrance]

Wow. How quickly this thread went off track.
Question: Is Ireland part of the Schengen Agreement? If so, there are no quarantine rules for taking a dog there. It's not; however, Ireland appears to be fairly dog-friendly. "To bring a dog to Ireland from the US, your dog must be microchipped, have a valid rabies vaccination (administered after microchipping), and an EU pet passport or health certificate; you will also need to have your dog treated for tapeworms before arrival, and must enter Ireland through a designated port like Dublin Airport or Rosslare Europort to undergo compliance checks upon entry. "

I don't know where you are located, but I can recommend Candice Manganaro, DVD, of Park Heights Animal Care in Fruitland Park if you are in TV. She has handled our two and many others' dogs for traveling outside of the US and knows all the requirements.

Aside from having to get a health certificate within ten days of air travel, there must be an APHIS stamp (Animal and Plant Health Inspection Service) from the Dept. of Agriculture. This used to be available by taking the vet's health cert to Gainesville and walking out with a stamp, but since Covid it's done by mail now. Your stamp could come from anywhere, and you must pay for FedEx or UPS to have it mailed to you. Also, Dr. Manganaro had the right email to "complain" to when our stamp was late in arriving. She can also handle the UPS mailing (costs about $80).

Then there are certain things to be done before coming back home to the US. We always had to visit our vet in France for a health cert and to fill out the proper forms. A deworming pill had to be administered by the vet despite the fact that the dog(s) were already protected for it. It was called a pet passport, but really, it's just the paperwork you need to get back into the US.

We used to fly our Golden Orlando to Frankfurt, Germany, because it was nonstop.Then drive him to France. We would go through all. that. stuff. I guess Lufthansa checked it on the US end, but they never checked it in Germany. He would come off on the large luggage conveyor between sets of golf clubs, and away we would go.
Coming back to the US was a different story. They checked everything, down to his toenails.