Who can do the 12-month body-protected area test?

The standard says what the routine inspection and test covers and that it happens at intervals not exceeding 12 months. Who does it is set by your state or country, and by what your accreditation scheme accepts, not by AS/NZS 3003 itself.

In Victoria the routine test involves no installation work, so Energy Safe Victoria treats it as outside the prescribed-work system; in practice it is usually done by an M class licensed electrical inspector, who knows the tests and fits the label. In New Zealand the annual check is done by a registered electrical inspector, who issues a Record of Inspection, and the RNZCGP accreditation standard asks for exactly that document. In the other Australian states it is commonly done by a licensed electrician or by a biomedical testing company that tests the equipment on the same visit. Whoever does it needs an RCD tester that can perform the AS/NZS 3003 tests, which some common testers cannot.

Whoever you use, keep the test report with the classification record, make sure the new label goes on the sign, and check that your accreditation body and insurer accept it. If in doubt, ask your state regulator.