Oracle 11g database copy
Once you've installed the Database Instance onto your other PC:

Use SQL Developer's "Database Copy" to copy straight from one to the other, or "Database Export" to simply export the source database into file(s).
They're available in the "Tools" menu.

Both instances should be running if you choose "Database Copy."

If you choose "Database Export," you can choose to have it all go to one or the other.

Beware of disk space and wallet issues, and ensure your other instance's environment is ready to take the new structure/files.