Hi. I just thought I'd pop in to this board with my own experiences.
When I moved to the UK in 2008, I had an 8 year old sheltie that I'd had since he was a pup. The process of bringing a dog to the UK was a lot more complicated then, I hear, and crazy expensive, but I was determined not to re-home him. My pups are always like my babies, completely the center of my heart and family, loved to pieces. So, I brought him, and we spent his last six years on great walks in the Lakes and with all the love he was accustomed to.
But people often ask me if I would do it again, and I have to say no, never. The flight was pretty traumatic for him. He was panicked when we picked him up at the airport and remained like that for a few weeks. We both worked from home at the time, so he was always alone in a calm, quiet household (no other pets or kids, just lots of love from us), but he was still really overwhelmed and not himself at all for a long time. He developed really terrible separation anxiety, too. We couldn't leave him alone for ten minutes. Ultimately it took some months of gentle weaning (and a video baby monitor we could check from our smartphones) to get things normal again.
I feel kind of bad to warn people off it. Surely, some dogs will be just fine. Mine always was a bit timid to begin with. And we did have lots of good time together in his remaining years. But definitely don't underestimate how tough the flying can be on a pupper. Just thought I'd share it in case anyone else is sitting the fence on what to do with theirs.