Hi Alpha:
provided you know the design rules, anybody can design an approach. It must then be handed over to AsA for validation and flight checking, then it will be published and made available to Jeppesen/Garmin for coding etc.
This used to be the case but I think you'll find things have changed.
To design an approach in Australia, the designer, and design organisation, must now be certified under CASA Part 173. Although there were a number of organisations in Australia capable of designing approaches previously (using fully qualified and experienced designers) there wasn't enough new design work in Australlia to justify the cost for all these organisations to install and maintain the rigorous QA infrastructure requirements on a full time basis to maintain certification under the new Part 173.
Result? The only organisation that is now certified and approved for designing approaches in Australia is Airserivces Australia, which means no price competition for the industry and long delays for designing or amending approaches. This is a good example of over zealous regulation killing off competition and choice, particularly considering that there has never been a safety issue related to poor procedure design in Australia to the best of anyone's knowledge.
Hart Aviation and, I think, IAS used to be certified but are no longer. Ambidji designs instrument charts but only for international jurisdictions where Part 173 is not applicable. IDS (Brisbane based) design charts for the Australian DOD (?) and Strategic Airspace (Sydney based) is another capable design organisation but its current involvement in procedure design is not known. And there may be others.