I have no idea of the rules in Turkey, but when I brought my lovely Peke to Amsterdam
from Saudi Arabia I was amazed to find I could have her fly with me in a small transit carrier. It uis supposed to be able to fit under the seat but wouldnt quite so they put her in the Toliet for take off. They put her by the galley then but she howled, the cabin crew asked if she would be better on my lap! One happy little dog snoring away and I was so HOT!
I know that Air France also allows dogs in the Cabin if small enough.
I couldnt leave mine behind if I moved permanently