Dan Marsden was working to add Quiz support to Moodle's plagiarism checking system (https://tracker.moodle.org/browse/MDL-32226). That might include this.
Or, you could use a plugin like https://moodle.org/plugins/quiz_archive or https://moodle.org/plugins/quiz_answersheets + https://github.com/moodleou/save-answersheets to extract all the quiz responses into files, which could then be fed to the plagiarism system.