To quote from the link provided by Greg W
Section 8 of the Parliamentary Privileges Act 1987 provides that the House does not have power to expel a Member. Before this provision was enacted the House had the power to expel Members derived from the privileges and practice of the House of Commons passed to the Australian Parliament under section 49 of the Constitution.
The House of Representatives expelled a Member on one occasion only. On 11 November 1920, the Prime Minister moved:
That, in the opinion of this House, the honorable Member for Kalgoorlie, the Honorable Hugh Mahon, having, by seditious and disloyal utterances at a public meeting on Sunday last, been guilty of conduct unfitting him to remain a Member of this House and inconsistent with the oath of allegiance which he has taken as a Member of this House, be expelled this House.
The speech to which the motion referred was delivered at a public meeting in Melbourne, and concerned British policy in Ireland at that time. The Leader of the Opposition moved an amendment to the effect that the allegations against Mr Mahon should not be dealt with by the House, and that a charge of sedition should be tried before a court, but the amendment was negatived and the original motion was agreed to on division.132 After the motion of expulsion was agreed to, a further motion was moved declaring the seat vacant which was agreed to on division.133 Mr Mahon stood for re-election in the resulting by-election but was not successful.
As we can see, from 1987 it is impossible for the Australian Parliament to expel a Member. However recent events may bring the discussion of whether options should be introduced to allow expulsion in extreme cases.
Edit: To address Phoog's question about in the case of criminal activity, this would fall under the section "Qualifications and Disqualifications".
A person is incapable of being chosen or of sitting as a Member of the House of Representatives if the person:
- is a subject or citizen of a foreign power or is under an acknowledgment of allegiance, obedience or adherence to a foreign power;
- is attainted (convicted) of treason;
- has been convicted and is under sentence or subject to be sentenced for an offence punishable by imprisonment for one year or longer under a State or Commonwealth law;
The second and third points are the relevant ones for Phoog's question. Treason is an absolute exclusion, while the third point would only apply between conviction and completion of that sentence (provided the sentence is 1 year or greater).