Thanks to @Aryan Raj suggestion, here is a more explicit solution to my problem. Add the following lines to the Dockerfile:

# Add Tini
RUN apt-get install -y tini

# Set Tini as entrypoint
ENTRYPOINT ["/usr/bin/tini", "--"]

# Set your main application as CMD
CMD ["/usr/queue/qserver", "--port=1234"]

Now the qserver daemon runs as expected in the background!