HornetQ doesn't have any kind of DR backup functionality. You can either implement a manual procedure where you stop the broker and back up the data (backing up the data while the broker is running is not recommended) or you can use the network replication HA functionality to create a copy of the journal on another machine during runtime.
Would I be correct in assuming that, since HornetQ supports shared-storage failover, snapshot backups using LVM or similar will work?
I don't have any experience with that so I couldn't say. Feel free to give it a try and report back with the results.