Abortion in Australia remains a subject of state law rather than national law.
The grounds on which abortion is permitted in Australia vary from state to state. In every state abortion is legal to ‘protect the life and health of the woman’, although each state has a different definition. Note: The phrase to 'protect the life and health of the woman' has come to mean 'on request of the woman'.
There is no law anywhere in Australia that requires the notification or consent of a woman's partner.
There is no enforced waiting period for an abortion and a minor does not require parental consent or notification for an abortion - except in Western Australia.
State-by-state (and territory) legality of abortion in Australia
Australian Capital Territory: Abortion law in the Australian Capital Territory was for many years governed by case law and the criminal code of New South Wales. However, in 2002, it became the first jurisdiction in Australia to legalise abortion in full (throughout entire pregnancy), when the Stanhope ALP government, with the assistance of Green and independent members, passed the Crimes (Abolition of Offence of Abortion) Act 2002, removing abortion from the criminal statute books altogether; or said plainly, abortion is legal up to birth.
New South Wales: Abortion law in New South Wales is primarily based upon the Levine ruling of 1971 (itself derived from the Victorian Menhennitt ruling of 1969), which declared abortion to be legal if a doctor found 'any economic, social or medical ground or reason' that an abortion was required to avoid a 'serious danger to the pregnant woman's life or to her physical or mental health' at any point during pregnancy. This was expanded by the Kirby ruling of 1994, which extended the period during which health concerns might be considered from the duration of pregnancy to any period during the woman's life.
An upgraded law passed 8 June 2018 criminalises anyone protesting within 150 metres of an abortion clinic ("protest free zones"). It is deemed an offense to offer pregnant women (and/or accompanying people) within these zones, information related to pregnancy, help and assistance, as well as film, stand or even pray. Protesters face jail time up to 6 months and fine of $5,500 for first offense and 1 year jail and $11,000 fine for subsequent offense.  [1A]
Northern Territory: Legislation in 1974, based on earlier legislation in South Australia and the United Kingdom, legalised abortion in the Northern Territory if the risk to the woman's life or health is greater than it would be if the pregnancy were not terminated and it is likely that the child will be physically or mental handicapped. The abortion must be approved by two medical practitioners and must be performed in a hospital. Abortions must be performed during the first fourteen weeks of pregnancy, except when there is a case of serious risk to the woman's health, when abortions are allowed up to the 23rd week.
South Australia: Medical sbortion of pregnancy became legal in South Australia in 1969 under the Criminal Law Consolidation Act, when necessary to protect the life or physical or mental health of the woman - taking into account the current and reasonably foreseeable future - or in cases when the child was likely to be born with serious handicaps. However, the reality is, South Australia now has a situation similar to other states, where women can have an abortion on request.
In SA abortions may be performed by doctors up to 28 weeks. Abortions must be performed in a hospital and be approved by two physicians, and are also subject to a residency requirement. The hospital, dual approval and residency requirement may be waived in an emergency. The term "emergency" is used broadly though, and, according to some staff, has been abused by some doctors.
Queensland: The McGuire ruling of 1986 declared abortion to be legal if necessary to preserve the woman from a serious danger to her life or health - beyond the normal dangers of pregnancy and childbirth - that would result if the pregnancy continued, and is not disproportionate to the danger being averted. Abortion law in Queensland closely mirrors the law in Victoria. That being said, abortions are carried out as "therapeutic miscarriages", performed by specialists, upon request of the patient after an appointment with their local GP. This procedure is only applicable on pregnancies under 22 weeks and is partly covered by Medicare or more-so by private healthcare insurers. In addition to this, abortions can be performed if a foetal defect is considered to be "inconsistent with life" - this has been narrowly interpreted to mean that the newborn would die immediately or shortly after birth.
Tasmania: In Tasmania, since 21 November 2013, abortions are allowed on request up to 16 weeks of pregnancy, with abortions after that time requiring consent of two doctors on medical or psychological grounds. The law also criminalises filming, intimidation and protests against patients within 150 metres of abortion clinics ("protest free zones"). See above NSW definition "protest free zones"
Abortion is legal up to birth requiring two doctors to agree that it is appropriate.
Victoria: Sweeping changes to abortion laws were passed on 10th October, 2008, after Premier John Brumby announced "our existing laws are out of step with community sentiment."  Current legislation now allows abortion up to full term (birth). That is, abortions up to 24 weeks on request, with abortions after that time until birth requiring two doctors to agree that it is appropriate,based on the women's current and future physical, psychological and social circumstances. This was passed by the Upper House 23-17  , with no amendments.
Doctors who conscientiously oppose abortion have to refer women requesting an abortion to doctors who perform abortions or face prosecution. No anaesthetic needs to be given to aborted unborn babies at any stage of development.
Since 2016, it is an offence in Victoria to protest within 150 metres from any medical centre. These are called "protest free zones". See above NSW definition "protest free zones"
Western Australia: An abortion bill passed, subject to certain amendments, on May 20, 1998, allowing abortions to be performed up to 20 weeks of pregnancy on request - subject to counselling by a medical practitioner other than the one performing the abortion - or when serious personal, family or social consequences will result to the woman if an abortion is not performed, when the life or physical or mental health of the woman is endangered and when the pregnancy causes serious danger to the woman's mental health. Abortions after 20 weeks of pregnancy may only be performed if the child is likely to be born with severe medical problems - which must be confirmed by two independently appointed doctors. In the event of the woman being under 16 years of age one of her parents must be notified, except where permission has been granted by the Children's Court or the woman does not live with her parents.