Michelle Pearson said the suicide of Dolly brought back many difficult memories about her son.
Ms Pearson urged politicians to "get the ball rolling" as Australia was "losing too many precious kids, way too many" to suicide.
According to the Bully Zero Australia Foundation, Victoria is the only state where bullying is a crime.
In other states, stalking and harassment laws cover some elements of Victoria’s Act but there is no specific law that makes bullying a crime.
"Every step must be taken to reduce the incidence of bullying, whether offline or on, and eliminate it wherever we can," Mr Turnbull wrote in a Facebook post.
"Much more work is needed from governments, health groups and the internet companies themselves to prevent cyberbullying, stop it when it occurs and to minimise its impact when it does occur."
A Queensland mother's petition to ban an app with potential for cyberbullying has amassed more than 101,000 signatures in five days.
The petition by Katrina, who does not disclose her last name, gained huge traction following the tragic death of Northern Territory teen Dolly Everett who took her own life and calls for the app Sarahah to be banned.
"I do not want my daughter or any other to become the next Dolly," the Rockhampton mother wrote in the petition's description.
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14, Suicide Call Back Service on 1300 659 467 and Kids Helpline on 1800 55 1800 (for young people aged 5 to 25).
