To add on top of @aleveille’s suggestion: if you don’t prefer to screen ... into the Docker VM, you can use mounts from /Users/ and /var/lib/docker/ to perform backups, e.g. like this:
docker run --rm -it -v /Users/<username>/volume-backup:/backup -v /var/lib/docker:/docker alpine:edge tar cfz /backup/volumes.tgz /docker/volumes/
Maybe there will be an easy way to add volume plugins so that we don’t have to manually access the VM’s file system.