Daniel Billings, 31, was sentenced to a maximum of 28 years' jail for Ms Ticehurst's murder, which was an act of revenge for reporting allegations of rape to police.
NSW Supreme Court Justice Natalie Adams set a non-parole period of 20 years, a sentence widely criticised for being too lenient.
Billings was out on bail and subject to an apprehended violence order when he smashed into Ms Ticehurst's bedroom window at her house in Forbes, in central western NSW, and stabbed her 15 times in April 2024.
While the NSW Office of the Director of Public Prosecutions (ODPP) on Friday said it would not challenge the sentence, Billings filed an eleventh-hour notice of intention to appeal.
The document was filed late on Friday and he has one year to lodge a notice of appeal.
Ms Ticehurst's father Tony was told of the ODPP's decision not to challenge the sentence, but only found out about Billings' bid through the media, Orange independent MP Philip Donato said.
The family already endured delays of more than 800 days to see Billings sentenced, including more than 18 months of closed-door legal negotiations.
"No legal process can undo the Ticehurst family's loss, but the system can at least keep (Mr Ticehurst) informed and stop blindsiding him," Mr Donato said in a statement.
"There is clear and inexcusable inequity and I'm calling the ODPP out on this; it's simply not good enough."
The ODPP has been contacted for comment.
Premier Chris Minns said Billings was a "despicable" killer, who should rot in jail.
"There's always the chance when you pursue an appeal that a higher court imposes a longer penalty, and I certainly hope that happens," Mr Minns told Sydney radio 2GB on Tuesday.
Billings' move to appeal also dashes family hopes of getting timely answers about Ms Ticehurst's interactions with domestic violence services in the lead-up to her death.
Her mother Kate Shaw urged the premier to release a government report into her contact with the state's Staying Home Leaving Violence program, designed to help victims boost their home security.
"She was my only child, was much loved and is sorely missed by me, her father Tony, her son, her extended family and many friends," Ms Shaw said in a statement when Billings was jailed.
The premier has previously said the review would be released once the legal process was finalised, including any appeals.
Ms Ticehurst reported Billings to police in early April 2024 after months of threats, violence and abuse.
Billings was arrested and charged with a string of sexual assault and domestic violence offences, but was freed on bail by a local court registrar a fortnight before the murder.
Upon his conditional release, Billings became enraged and obsessed with a belief he had been wrongfully accused of rape and formed a plan to kill her.
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