This is the part of data cabling almost nobody knows to ask about, and it is the single most useful question you can put to whoever quotes you.
An electrical licence covers electrical work. It does not cover cabling that connects to the telecommunications network. That is regulated separately by the ACMA under the Cabling Provider Rules, and it has to be carried out by a registered cabler. The two qualifications are different, and holding one does not grant the other. Plenty of licensed electricians are not registered cablers, and plenty of people who pull data cable for a living hold no electrical licence at all.
Registration comes in three scopes. Open registration covers structured cabling, fibre and commercial work, and is what a full network installation calls for. Restricted registration covers smaller domestic work, such as an extension or cabling behind a modem or alarm panel. Lift registration covers cabling in lifts. Getting registered requires documented supervised experience, currently 360 hours, on top of the training itself.
The work itself is governed by AS/CA S009, the customer cabling wiring rules, currently the 2020 edition. It sets out how cabling is installed, how it is separated from other services, how it is labelled and what has to be tested. It is a real standard with real obligations, not a guideline.
None of this is exotic. It is simply a rule most homeowners have never heard of, which is exactly why it is worth checking. Ask for a cabler registration number the same way you would ask for a licence number, and be wary of anyone who treats the question as unusual.