We moved two cats from the US to Asia and are now looking to move four cats from Asia to the UK. By far and away, moving our pets is the most stressful part of the international move experience. It will be hard, and stressful, but it will likely be ok. The statistics for moving pets are on your side.
I can't be of much help with the process, as we are using a pet relocation company, but I wish you luck!