If you're just considering Docker on a single host, then there's very little difference between the Docker case and the non-Docker case. All you need to do is tell Docker which directory on the host filesystem to map into the Docker container running an MQ queue manager. From there on, the storage management is exactly the same.
Things change if you are using Containers as a Service (CaaS) such as Kubernetes or Docker Swarm. In this case, you have a set of hosts, and your MQ queue manager could be scheduled onto any host. In the case of a host failure, the CaaS re-schedules your container onto a different host, and needs to be paired back with the same storage, usually using networked storage. There are multiple types of networked storage available: block storage, such as Ceph RBD, AWS EBS, OpenStack Cinder or Bluemix Block Storage; or networked filesystems such as NFSv4, CephFS, GlusterFS, AWS EFS, OpenStack Manila, or Bluemix File Storage. For MQ, block storage is probably the safest choice, if you can. The networked filesystems are very much usable as well, but you may need to run your own additional testing to check compatibility, similar to what is required for MQ multi-instance queue managers.