The VHF air band can never legally be used for chat.
Even 123.45 is limited to air-to-air by "aircraft engaged in flights over remote and oceanic areas out of range of VHF ground stations to exchange necessary operational information and to facilitate the resolution of operational problems". (AIP Gen 3.4 - 3.1.5)
To return to the original question, I can't find anywhere in AIP which suggests someone can have a personal frequency. All licensing is through ACMA. Even if you got a freq from them, it would be limited to operational broadcasts.
John Brandon lays it out well on the RAAus site:
An aircraft station may only be operated (i.e. transmitting) when it is on board an aircraft, thus you cannot operate your hand-held transceiver as an aircraft station unless you are in an aircraft and identify yourself with that aircraft's station call sign. If any condition of CL2006 is breached (for example, transmitting on a frequency not encompassed by the class licence) the operator is no longer authorised to operate under the class licence. In this instance, the operator would be liable for prosecution by the ACMA.
An aeronautical mobile station (and an aircraft station) may only be used for communications that relate to:
the safe and expeditious conduct of a flight
an emergency
a matter that relates to the particular occupation or industry in which the aircraft to which the aircraft station relates is engaged; or the aeronautical mobile station is engaged.
Typically a flight instructor on the ground with a hand-held transceiver supervising a student in the circuit is operating as an aeronautical mobile station. The same might apply to a person advising traffic conditions at a fly-in. The operator of an aeronautical mobile station must use a form of identification that clearly identifies the mobile station.
Hope that clears it up. You can be prosecuted and have your radio operators license taken away for chatting, or using a frequency for which you are not licensed.