Nancy Nutmeg, the heroine, is a poor Irish washerwoman with a wooden leg, who works hard to support herself and her grand-pappy, Old Nugget Nutmeg, a retired pirate who spends most of his time up a pine tree. Nugget has a pair of magic spectacles, the Specs o' Gold, which he won from a leprechaun, which show the wearer any gold. But there is no gold to prove it.
His old pirate shipmates drop in for a visit, on their way to the goldfields of New Zealand. Nugget shows them the specs. The greedy Captain Long John Knickers, realising they are magic, decides he wants them for himself. Nugget runs off with the pirates but drops the magic specs on the path down the cliff, where Nancy finds them.
Nancy has a tantrum and smashes the furniture. Then she has an idea, and converts her washtub into a boat, and sails away. She soon runs out of oil and trades for some with Corky Screw, a miner and inventor, who has a submarine shark, the Cutty Shark. Nancy tricks him, and he becomes her enemy. A lucky charm saves her life.
She makes friends with the Great White Whale who is also travelling to New Zealand. But Corky Screw harpoons the whale, off the coast of Nothern Australia. Nancy saves his life and nurses him. She gathers food and has a battle with crocodiles. Eventually she arrives in New Zealand and sails down the West Coast where she makes a camp.
A thieving kea latches on to her, and eggs she gathered in Australia hatch into crocodiles who call her 'mummy'. She finds and buries the skeletons of a miner and his horse and finds a diary with a map of the road. She finds a giant moa egg and captures the mother moa. She converts her washtub into a wagon using the wheels of the miner's wagon and sets off to the road. Trying to read the map in the miner's diary with the Specs o' Gold she discovers rainbows, leading to gold nuggets.
She is captured by the Laughing Dog people but makes friends with the leader, Princess Puha. They both knew the Great White Whale. Nancy carries on to Golden Gully where she learns that Nugget has been trapped in an avalanche on Mount Devilshorn. She climbs the mountain and rescues him. They are both rescued by the Flying Hat Circus who travel by hot air balloon. Nancy spies a huge rainbow coming from an island in the lake, using the magic specs.
Nancy returns the Specs o' Gold to Nugget, but he and his mate Hoppy get gold fever. Corky Screw has traveled upriver to Golden Gully where he captures Nugget and Hoppy, taking them to his island lair.
Nancy follows in the circus balloon and sets a booby trap for Corky. She rescues Nugget and Hoppy from a sinking raft and the Laughing Dog people from a burning canoe, and they all celebrate at a wedding feast. Nancy is persuaded to take over the Salty Dog and to set sail chasing Cap'n Long John, who has escaped jail and has converted his fellow prisoners to the Cutthroat Convict Crew and escaped in a stolen ship, the Slippery Mermaid, which is where the story continues in the sequel 'The Voyage of the Salty Dog'.