Google Tasks can not set a repeat, but DoTasks can set a repeat.
Tasks that set a repeat will automatically create the next task when the due or reminder date is today. You can not set a repeat for the tasks that have not set due reminder. If an end date is set, tasks after the end date are not created.
In the task list screen, the task with yellow repeat icon is enabled. This is the latest task that set a repeat. If there is no enabled repeat, the next task is not automatically created.
If the task that has the parent, the automatically created task also has the same parent.