I've collected three dogs that were shipped, this past year; one a domestic flight -- Henry, the rescue in CA that Amanda fostered for a while -- and the other two flights from EU countries.
In none of the three instances did I see any evidence of a bad experience. The international flights were a long time in the crate for the dogs, but they seemed fine afterwards. Both are now show dogs, with finished CH titles.
When you ship international, you will want to find someone who has had experience with various airlines. Some are better than others, and breeders and show people who fly dogs regularly will know that. Air France is one of the better ones, I believe; but I don't know a thing beyond that!
A dog shipped domestically OR internationally must be in a crate of the size and type specified by the carrying airline; there must be food and water in the crate in airline-approved containers. The crate may not be opened by anyone until the dog has reached the destination and cleared Customs, if an international flight.
Clearing Customs takes a lot of time, since a Centers for Disease Control doctor has to examine the dog and its health records, which are shipped on the crate with it.
I suggest you find out which airline you will be using, and contact them with questions. All my experiences with carrying airlines have been quite positive. I hope you find the same.
I would not hesitate to ship any of my dogs, if the alternative was leaving them behind on another continent. JMO.