The girl was left with permanent brain damage after her father, then 25, shook her as he fed her in November 2018.

The girl's mother returned from a shower to the sounds of the baby's high-pitched screams and cries, and spent an hour trying to settle the girl.

The infant was taken to hospital 12 hours later, where her severe injuries were identified.

Campbelltown judge Andrew Colefax jailed the father for one year and nine months after granting him a 50 per cent discount for belated admissions to police and an early guilty plea to the charge of recklessly causing grievous bodily harm.

The non-parole period was one year.

That August 2020 decision was upended on Friday when the NSW Court of Criminal Appeal agreed with prosecutors that it was manifestly inadequate and had other legal errors.

A key issue was Judge Colefax's assessment that the seriousness of the crime was below the mid-range for such offences.

He accepted submissions that the offence was "one-off", unplanned and brief.

While acknowledging Judge Colefax ran a busy court, the crime was significantly more serious than he'd appreciated, the appeal court said.

"She was utterly defenceless and completely dependent upon her parents," Justice Robert Allan Hulme said on Friday

"The respondent was a mature adult. He was not lacking in intelligence and he told police he was aware that shaking a child could have serious effects.

"There is nothing that remotely explains his actions of shaking the baby so that, as he described to police, her body movements were 'like a ragdoll, I suppose'."

Granting a 25 per cent discount for the early plea, Justice Hulme resentenced the father to a minimum of three years in jail.

The offender was genuinely remorseful and had good prospects of rehabilitation but sending a message to the community about the offending was "quite significant", the judge said.

The offender's full term of four-and-a-half years will expire in February 2025.

Australian Associated Press