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)