I have configured my annotations in okular for highlighting text in PDF's and so on, to a large extent.

Now I just got a new laptop and installed things from scratch, it would be nice to be able to copy the config for okular from my old laptop so I don't have to re-do this.

Does anyone know how to?

that is ~/.kde[4]/share/config/okularpartrc but you may also want the okularrc file in that folder and possibly part.rc and shell.rc in ~/.kde[4]/share/apps/okular/ if you want both instances to be identical

why not copy your entire KDE config ~/.kde[4]/share/config and maybe apps ? there will be some parts like akonadi and your Amarok collection that you probably won't want.