Any event organiser can be a first party verifier of their own organisation.
Organizations and individuals can become Second Party verifiers if they meet prescribed competencies set down by industry. Precedents in other auditing/verifying systems show that a minimum of four years documented and proven practical experience in the sector being audited must be held. Additionally, it is likely the industry (and particularly the Sustainable Event Alliance) will set down parameters for this and potentially also a competency exam. This will prevent people or organisations with limited demonstrated experience in events, sustainable development, applied sustainability and management systems, from setting themselves up as verifiers.
Unless your organisation is already an accredited auditing/certifier against ISO standards it is unlikely you will look at becoming an third party verifier as this is an arduous process and the potential number of clients in Australia would not warrant the effort.