Advise on moving a Dog international?

I am moving from Ohio to Sri Lanka. I really want to take my 19 pound Beagle with me ON board. It is too long a flight for her to go as Cargo. Do you know anything about taking a dog on board. She doesn't bark and she has been fine on long drives (8hours). I would need to stop in Europe and then On to Sri Lanka. Do you know anything about airports in Europe and rules, since I will have to walk her at that point.