In 1975, a young woman, Robyn Davidson, arrived in Alice Springs with an unusual expedition in mind:

she intended to walk 1700 miles across the deadly Australian desert to the Indian Ocean, with just her dog Diggity for company and three camels to carry her gear. No-one took her seriously.

But she made it. And Davidson's adventure, covered by the National Geographic and later in her book Tracks, turned her into an Australian icon. It's a terrific, inspiring story of a no-nonsense, slightly out-of-place woman who could articulate no greater reasons for her dangerous journey than "why not?" and "I would like to think that an ordinary person is capable of anything".

Something of that purity of intent lends itself to this beautiful film. It's more than 40 years since Walkabout, Nic Roeg's masterful account of a young woman's self-discovery in the outback; this makes for an equally memorable companion piece.

In her mid-twenties Davidson (Mia Wasikowska) wants to escape city life. Her voiceover tells us of disappointment with the "self-indulgent negativity that is the malaise of my generation, my sex, my class". When she's around others, particular those of her own age, she looks as though she wants to crawl under a stone.

The film follows her two years in Alice Springs, learning how to tame and work with camels, at first with an irascible Austrian camel breeder, more helpfully with an Afghani camel wrangler, much of whose advice will serve her well on the long trek. In dire need of funds, she reluctantly agrees to sell her story to the National Geographic, whose photographer Rick Smoland (Adam Driver) will join her at designated stages along the route.

On the journey itself, the indefatigable walker who came to be known as "the camel lady" has to contend with the scorching sun (Wasikowska's skin goes through a complete spectrum from wholesome tan to blistering sunburn), lack of water, rampaging wild camels and - for her the worst irritant of all - the appearances of Rick, who talks too much and wears absurd shorts and annoys the hell out of her, even after he satisfies some of her more urgent needs.

But Davidson's desire to be alone is a carapace of sorts, concealing deeper feelings of loss and loneliness. And there are lovely scenes with those she finds more appealing: the aboriginal elder, Mr Eddy, who guides her through sacred land; the lone white man who lives in the middle of nowhere and feels that words are overrated; an elderly couple who offer a brief and blissful respite. By the conclusion of the film, this young woman's motivations become more complex, deeper and infinitely more touching than those of a rebel longing to be alone.

The luminous Wasikowska perfectly embodies her countrywoman, conveying an intensely self-contained nature that is at once down-to-earth and mysterious. The Australian first demonstrated herself as a dab hand at spiky intolerance in her break-out role in TV's In Treatment (as a younger teenager whose outward strength also hid vulnerability) and she's spectacularly prickly here, whether towards tourists or her photographer shadow. But when she smiles, she's a heartbreaker.

Director John Curran and his cinematographer Mandy Walker make hay with the Australian landscape, with one gorgeous image after another, accompanied by Garth Stevenson's piano-dominated, deftly expressive soundtrack. By the time Wasikowska and her camels enter the corner of a pure white frame - the sandy desert that might have been a clear sky - we've been so utterly seduced that we're ready to pack our bags for our own adventure.