All data for Wikibase and the Query Service is stored in Docker volumes. You can create compressed copies of these volumes to use as backups or to hand off to other users.
Volume backups will only work if you use the same image when restoring / using the backup data. If you are backing up your mysql data you may also want to just take an SQL dump.
You can see all Docker volumes created by using the following command:
docker volume ls | grep wikibase-docker
You can grab a zip of each volumes by doing the following:
docker run -v wikibase-docker_mediawiki-mysql-data:/volume -v /tmp/wikibase-data:/backup --rm loomchild/volume-backup backup mediawiki-mysql-data
You, or someone else, can then restore the volume by doing the following:
docker run -v wikibase-docker_mediawiki-mysql-data:/volume -v /tmp/wikibase-data:/backup --rm loomchild/volume-backup restore mediawiki-mysql-data
If using volume-backup for the database does not work because of InnoDB tables (check here), you can achieve data backup using mysqldump.
docker exec wikibase-docker_mysql_1 mysqldump -u wikiuser -psqlpass my_wiki > backup.sql
docker exec wikibase-docker_mysql_1 mysql -u wikiuser -psqlpass my_wiki < backup.sql