What does the policy say? The answer is: it depends.
You cannot be appointed as a Principal Supervisor without being registered on the MQSR. This rule is the same for Associate Supervisors. (An Associate Supervisor is a person with a lesser fractional supervisory load and responsibility compared to the Principal Supervisor).
You can be appointed as an Co-Supervisor (an academic staff member who has not supervised a HDR candidate to completion, or who is on an appointment of less than three years. Co-supervisors work under the direction of a Principal Supervisor.) without being registered on the MQSR. This allows you to develop your skills as a supervisor, and it also provides you with an opportunity to develop all the criteria of appointment to Principal Supervisor so that you can become registered.
MQ Policy does not stipulate that you must be registered on the MQSR to supervise an MRes candidate (but see the 'however' below).
Some Faculties require all supervisors, regardless of role, to be registered on the MQSR. You MUST check with your Associate Dean HDR, or your School Director HDR to find out your local policy.