It's hoped 'Coco's Law' will be introduced as soon as possible, to protect victims of online bullying and to save lives.
The proposed legislation is being highlighted this weekend as it's the first anniversary since the death of Nicole Fox.
The 21-year-old from Clondalkin, Dublin died by suicide after being subjected to online harassment.
Since her death, her mother, Jackie, has launched a campaign to hold people responsible for their actions when it comes to cyberbullying.
She says the law named after her daughter is vitally needed.
"It's so vital because when Nicole was going through all torment and torture online, like so many others at the moment, the guards came to me and said their hands were tied.
"There was nothing they could do about it because there was no law against cyberbullying."