That was surprisingly easy: Just swaped the sonarqube:6.7-community for the sonarqube:7.9-community image entry in my docker-compose.yml and restarted the Docker container. Upon boot, the container restarted due to an error:

ERROR: [2] bootstrap checks failed[1]: max file descriptors [4096] for elasticsearch process is too low, increase to at least [65535][2]: max virtual memory areas vm.max_map_count [65530] is too low, increase to at least [262144]

This could be resolved by executing sudo sysctl -w vm.max_map_count=262144 on my Ubuntu 18.04 LTS / Docker Host. After another restart of the container, it worked and I could start the update using a webbrowser under http://IP:9000/setup

(also add the option vm.max_map_count=262144 to the /etc/sysctl.conf)