Yes you can take your pillow with yourself. Tough it is not generally seen in the flights, as they already provide you. But if you still want it, you can take it as hand carry.
Can I Bring My Own Pillow On The Airplane For A International Flight?
I'VE DONE THAT BEFORE! When I visited my great aunt in France. Just put it in your pillow in your suitcase and you'll be fine.
You don't have to stuff your pillow in a suitcase anymore or in a garbage bag. Check out www.kuddlekase.com its a wonderful project for people who travel with their pillow.