Tried this on webkit gtk 2.2.6. Open web inspector, go to Console tab. Focus on text box at the bottom of the screen where you can enter the commands. In this box, standard copy/paste shortcuts - Ctrl C and Ctrl V do not work.
Actually the keyboard shortcuts in general seems to be weird, on my AZERTY keyboard: Ctrl+A moves to the beginning, Ctrl+E moves to the end, Ctrl+T moves the previous character forwardt and follow it, except at the end where it swaps the last two characters.