There are many good routes to fly dogs and cats to Asia from Ireland. British Airways and Cathay Pacific would be the 2 main airlines as they fly direct and a direct flight is always better for pets. IPT can advise on the best routes for cats and dogs to travel to Asia.
In terms of veterinary preparation, Cats need to have had their full vaccinations (cat flu and enteritis) and dogs need to have had their full vaccinations against Distemper, Canine Hepatitis and Canine Parvovirus. All the vaccinations need to be given at least 14 days before the flight and not more than 12 months.
These often catch people out as some parts of the vaccines can be given every 3 years, so the owners think that their pets are fully covered, but actually for the purposes of entry of cats and dogs into Asia, all the fractions need to be given within 12 months of the flight date and at least 14 days before the intended flight date.