Is there an exemption for parent volunteers or young helpers?

Access Canberra does not list parents as such. The exemptions it lists that can apply are:

• Close relatives: you are a close relative of the vulnerable person taking part, and all other vulnerable persons taking part are expected to be accompanied by their own relatives.
• Under 16: people under 16 years old do not need registration.
• Incidental contact: contact is incidental rather than regular (see the question on helping for a few days).
• Students: high school or secondary college students on work experience or a practical training course.

The Access Canberra page does not set out a separate exemption for volunteers. Volunteers are covered by the same test as paid workers.

Source: Access Canberra, Check if you need WWVP registration before applying.