CAO 20.91 is the go to guide.
You haven't mentioned whether you have the TSO129 430s, or the TSO146 430Ws.
14.1 The operator of an Australian aircraft to whom paragraph 14.2 applies is deemed to hold a navigation authorisation for:
(a) RNAV 5; and
(b) RNAV 1 and RNAV 2; and
(c) RNP 2; and
(d) RNP 1; and
(e) RNP APCH-LNAV.
14.2 This paragraph applies to the operator of an aircraft that is equipped, in accordance with paragraph 14.4, with equipment that was installed in accordance with paragraph 14.5.
14.3 It is a condition of the navigation authorisation that the aircraft is flown by a pilot in accordance with paragraph 14.6.
14.4 The aircraft must be equipped with a GNSS stand-alone system with en route, terminal and NPA capability having TSO-C129a or ETSO-C129a authorisation for Class A1.
14.5 The equipment must have been installed:
(a) if installed before 13 April 2005 — in accordance with CAAP 35-1; or
(b) if installed on or after 13 April 2005 — in accordance with CASA AC 21‑36 ( ).
You do NOT require an IRS/INS, you simply file that you do not have one. (ie C2 rather than C1 for RNAV2 approval). Remember this is 95% of the time, not 99.9999%... if you lose RAIM you are required to let ATC know as previously.
There are other limitations and requirements you need to be aware of (ie simply because as an operator with a correctly installed 129 unit, doesn't mean you tick the other boxes). Some items to consider (after reading 20.91) are crew training, system availability (how many satellites are in the GPS constellation at the moment), reporting required (CASA/ATSB) when intentionally or unintentionally deviating off track.
According to the CAO there are also some new restrictions relating to RNP APCH vs the previous RNAV/GNSS.
As always, accept PPRUNE advice with a grain of salt.