The pair were among a party of teachers who set out from Buka on Saturday morning to their jobs on the Cataret Islands, which lie 86 kilometres northeast of Bougainville.
A search is continuing for two people still missing after the boat took on water during attempts to refuel in heavy seas.
The manager of Bougainville’s Disaster Office, Franklin Lacey, said the mother and her 18-month-old drifted for about 30 kilometres before coming ashore.
“Somehow she got some debris from the sunken boat and got her baby on the debris and they floated.
“They floated to one of the islands in the Carteret Islands – Iangain Island. They are okay. They’re safe and sound on the island. They are with the health authorities on the island now.”
Lacey said three boats were still searching for the missing pair but five others also survived, although he was unsure how they came ashore due to patchy communication with the islands.
He said helicopters from the US Navy’s USNS Mercy also helped in the search.