Lucy May Popple is a seven-year-old English girl whose Yorkshire family immigrates to Adelaide, Australia, in the 1830s seeking farming opportunities. She greets Australia with enthusiasm and wonder, especially toward its unique wildlife, despite her family's deepening poverty. Lucy May maintains cheerful energy, often seeming unaware of their dire situation.

Her personality blends tomboyishness with feminine touches; she plays roughly outdoors and cares little for her appearance, yet frequently wears pink and styles her hair in braids. She forms profound bonds with animals, bringing her hamster Marsh from England and later adopting goats, sheep, and a dingo pup named Little, whom she domesticates against objections. She rescues and cares for native creatures like koalas and a wombat. This protectiveness defines her, causing intense distress when her father sells their sheep Snowflake for food money—an event contributing to later trauma.

Lucy May shows resilience and ingenuity, training Little or finding non-verbal ways to communicate with animals. However, she also displays self-centered impulsiveness, running away after Snowflake's sale. This triggers a carriage accident causing amnesia, partly stemming from a subconscious wish to forget the loss. During her memory loss, the wealthy Princeton family takes her in, mistaking her for a replacement for their deceased daughter, Emily. Despite the comfort, she prioritizes her biological family, attempting to negotiate farmland for them through her adoption.

Her Popple family relationships are central: she sees older sister Kate as a close companion and confidante, while viewing Clara as responsible but distant. She feels strong attachment to her parents, though hardships like her father's alcoholism strain this bond. Amnesia severs these connections, bringing nightmares of family rejection, though familiar elements like Little eventually trigger her memory's return.

A significant subplot sees her inadvertently aiding her family's escape from poverty. Moved by her loyalty during amnesia, the Princetons gift the Popples farmland after recognizing her selfless intention to secure their future. This resolves their financial struggles.

Throughout her journey, Lucy May faces educational challenges, struggling with academics like math, and societal conflicts such as her family's feud with wealthy Mr. Pettywell, which escalates when his dog kills one of her goats. She also displays perceptiveness, solving the theft of Mr. Pettywell's fortune by identifying his servant Adam's collusion with robbers.

Her character arc spans approximately four and a half years, concluding at age eleven with her role in uniting her family and achieving stability, symbolized by their journey toward a rainbow—a recurring motif of hope.