"We are planning to hold a celebration of Rye's life on July 10 in Hobart for family and friends."
Meanwhile, Edward James Rye was born last Monday night to Ms Brodribb.
"We wanted to give (Edward) a little nod to his uncle," she told The Mercury this week.
The 25-year-old backpacker went missing on May 21 after he separated from his travelling companion Mitchell Sheppard at the Rio airport.
They had an argument after the two took what is suspected to be a highly potent hallucinogen known as NBOMe.
The search for Mr Hunt started on social media when Ms Brodribb and her family could not contact him after he was last seen at the airport.
Police released CCTV footage showing Mr Hunt at the airport and a search led them to an apartment he booked for three days.
It then emerged he likely took a local drug that caused extreme paranoia and anxiety, and may have swum to an island 900m off the coast of Rio.