Hi, KKOB is correct. There's is no problem bringing a dog into Turkey so long as the paperwork is in order. The problem starts when you want to re-enter UK (and it IS only UK). HE/she will have to go into quarantine for 6 months even though all vaccines are up to date. UK says that the animal may have contracted rabies whilst in Turkey hence quarantine.
Long story, a friend of mine fell in love with a dog here and decided to take her home. VERY costly, very time-consuming to organise and she, the dog, eventually ended up living in Germany because, even though she was coming from/through Germany in theory, she still would have had to go into quarantine kennels for 6 months in the UK because she had been in Turkey. There is no way around it if they (the UK) know he/she has been in Turkey.