When we decided to move permanently to Turkey, we brought in 4 cats in two separate journeys travelling with Kibris (Cyprus Turkish Airlines) from Stansted. Few if any charter airlines will take pets. If Kibris does not work for you, Turkish Airlines from the UK (currently Heathrow and Manchester departures) to Istanbul , then a change of plane for the onward leg to Dalaman is a good alternative.
From the UK, Air France is not the best carrier since there are no direct flights on Air France from the UK to Turkey and their costs for animal carriage are at least twice that of UK carriers.
Kibris was excellent and the arrangements quite straightforward. Each pet must be accompanied by a fare paying passenger - hence our two journeys. The animals go in a special section of the hold, our cats went in regular cat boxes, no special crating required, and appeared on the luggage carousel at Dalaman 4 hours later, completely unpreturbed. 9 years later they are still here, enjoying life in the sun and have been joined by another half dozen or so local cats who have moved in over the years.
We have a friend who brought in two labs at the same time, same procedure and no problems. Both dogs quite unfazed by their adventure.
The most difficult part is co-ordinating your flight with all the certification needed. The carrier wont confirm the animal booking unless you have all the certificates and you cannot get the certificates more than 15 days in advance or they are invalid as they state that your animal is
currently healthy. If you can manage it, avoid travelling at peak holiday times - we did our journeys in May.
We did find that our local vet in the UK was unfamiliar with the regulations for importing animals, so we had to do all the research. The Turkish consulate in London was most helpful . Their number is 020 7589 0949 .
http://www.turkishconsulate.org.uk/en/questio.htm#takingpetstoturkey. There is quite a lot of running around involved as you need to have various certificates legalised by the Foreign Office etc but it isn''t complicated. Do allow about 2 weeks from start to finish.
We were flying on a Sunday and got the last piece of paper stamped at 4 p.m. on the Friday. We nearly didn''t make it as I had not realised that the Consulate was closed in the afternoon - but they made an exception and opened so I could collect the paperwork, so do plan your timings carefully.
When we arrived at Dalaman with the first two, I had files of paperwork for both cats ready to present to customs. The customs official peered into one of the boxes, said ''what a pretty cat, I love cats'', and waved me through, no papers were asked for and nothing checked but that was almost ten years ago and things are rather more professional now so it''s worth doing it all properly.
If you would like any further information, do send me a message.
Good Luck
Lantana