Shane Williams, 40, a paedophile with a 20-year history of crimes against children, was sentenced on Wednesday to 7½ years' imprisonment, with a non-parole period of 4½ years, for the attack that took place while the girl's mother sat on a computer nearby.

He will be eligible for release on parole in March 2018, subject to a decision by the Sentence Administration Board.

ACT Director of Public Prosecutions Jon White said on Friday his office would appeal the sentence.

"The DPP has today lodged an appeal against the sentence imposed on Mr Shane Williams, on the ground that the sentence is manifestly inadequate," he said.

"As the matter is now before the court, there will be no further comment."

The news comes as a Canberra mothers group, outraged by what it perceived as leniency, put pressure on the ACT government to toughen sentencing for child sex offences.

An online petition, started by a group called Canberra Mums, had already attracted more than 2600 signatures by 5pm on Thursday.

The webpage says the petition will be presented to "every official and government representative in Canberra and the federal government" once it collects 5000 supporters.

"We want a just sentence handed out," a spokeswoman said.

The spokeswoman said the group's members had been "so sickened" by the case they decided to take action.

Acting Attorney-General Katy Gallagher said the ACT government would respond to the petition, but emphasised sentencing was the legal system's responsibility.

"To the greatest degree, the sentence was actually a matter for the court," she said.

"I understand at times community response to sentences, either they support them or they don't support them … Sometimes they think the courts are too harsh and other times they're not hard enough."

Ms Gallagher also acknowledged some of the difficulties for people petitioning an issue that had "emotions attached to it".

"It is hard and I accept that," she said.

Williams was walking to a police station, where he was obliged to report regularly, when he went into the Belconnen Library to go to the toilet in September last year.

A three-year-old girl had walked away from her mother and came up to Williams in a friendly manner.

Williams told her to sit down with him, before sexually assaulting her.

The girl's mother came looking for her daughter and found Williams crouched behind her.

She screamed, and he ran off.

The offender was arrested some days later, and made full admissions to police.

Williams had been convicted of offences against children five times in the past, and had repeatedly returned to such crimes on release from prison.

He was drunk at the time of the offence. Williams had had a childhood of severe neglect, including physical and sexual abuse.

The maximum sentence for the charge of sexual intercourse with a minor is 17 years in jail.

Williams was afforded a 25 per cent discount on the charge for his early plea of guilty, as part of a standard practice designed to reward early pleas to all types of criminal offences.

ACT Law Society president Martin Hockridge acknowledged the sad circumstances of the case, but said the territory had comprehensive laws dealing with offences against children and the sentencing of offenders.

Mr Hockridge said the legislature set the maximum penalty for offences and the court then imposed a sentence.

"The courts must weigh all the evidence from both prosecution and defence and determine the seriousness of the offending behaviour," Mr Hockridge said.

"They are also required to take into account many factors, including the factual circumstances, the impact on the victim and any mitigating information concerning the offender, and come to a considered conclusion regarding the appropriate penalty.

"In circumstances where the prosecution takes the view that a sentence is insufficient an appeal can be lodged, allowing the sentence to be reviewed."

Bar Association president Greg Stretton, SC, said it would not be appropriate to comment on the particular case specifically.

But Mr Stretton said, in general, imposing a just sentence was difficult when the victim was a vulnerable member of society.

He said sentencing called on the court to balance a number of important purposes, including ensuring just and appropriate punishment, preventing crime, protecting the community, rehabilitating the offender, making the offender accountable, denouncing the offender's conduct, and recognising the harm to the victim.

"The law recognises that these factors do not all point in the same direction in each case,'' he said.

Mr Stretton said parole was a tool to promote good behaviour and foster rehabilitation because it was in the community and the offender's interests for the criminal to reform.

"The grant of parole in any case is no foregone conclusion and risks to the public assessed in terms of risks of reoffending are considered by the Sentence Administration Board in determining whether someone is released from jail at the expiration of the non-parole period.

''The effect of parole is that an offender is liable to be returned to jail if the offender does not comply with his or her parole obligations.''