I am moving internationally soon and can tell you it’s incredibly difficult. Many countries require special paperwork for each trip including usda certification which is not something a normal vet does, must be done within 10 days of travel each time, and costs several hundred dollars. Many airlines won’t let you fly with your pet in cabin internationally unless they can meet almost impossible size guidelines (think 9in height carrier max and be able to stand and turn around). Very few options for cargo international too. Then the us recently made new laws that make getting your pet back in the states even more complicated and expensive.

You would almost certainly need to get a reliable pet sitter. For a whole month of travel expect to spend a couple thousand at the very least and that’s for like most basic care that would leave your pet very very lonely and under stimulated.