Dolt has two options for backup: remotes and backups.
Using remotes for backups should be suitable for some use cases. Pushing to a remote creates an off server copy of the branch being pushed. Frequently pushing to a remote can serve as a reasonable backup.
Dolt also has backups, accessed with the dolt backup command. These backups look more like traditional database backups. The entire state of the database, including uncommitted changes, are copied to another location.