I moved my dog from the US to Norway. He's small, but was JUST too large to be able to travel in-cabin with me.
The paperwork was intense. It was a lot of work getting all his vaccinations and preventative medications done in the right order, at the right time before travel, signed by the right people. Even had to get him a second microchip because the one he had was not an internationally recognized standard and wouldn't be recognized by standard European chip readers.
Now some of this is because I was moving from a rabies-endemic country to a rabies-free country. But honestly, if I ever travel internationally with the dogs again (for vacation, not another big, long-term move), I'll be sticking to ones we can drive to and/or have very, very easy border crossing requirements for dogs. I personally found it WAY too much work and stress to go through for a short-term trip, for both me and my dog.
Also be very aware of any breed restrictions/bans at your destination. If we'd had a dog that even sort of looked like an APBT or AmStaff (and not, y'know, a poodle), there's a high chance it would've been denied entry into Norway. It sucks and I don't agree with it, but it's how things work here.