Use the Project Archiver (under the File menu) to port the project file and its associated media to an external hard drive. And then always work on the project file that's on the hard drive, as you move from computer to computer.
BTW, project files aren't universal, by the way. You can't work on a version 12 project file in version 11 or vice versa. And you can't work on a Windows project file on a Mac and vice versa.