‘Cosmic power’: Sea and Sky, c1936 by Emily Carr. Photograph: Art Gallery of Greater Victoria

If ever there was a heroine of true grit in the history of art it was Emily Carr, a painter of such singular strength and beauty it is almost impossible to believe that the revelatory exhibition at Dulwich Picture Gallery is her first in this country. Carr’s landscapes of the high skies, wild bays and deep forests of the Pacific west coast of Canada – whispering with sound, radiant with inner movement and mysterious light – are as exhilarating as the places they represent.

Carr found a new way of painting that is unlike any other, in which the vision is radically joyful and modern, the paint as fine yet potent as the breezy air around her. Although she is often compared with her contemporary, Georgia O’Keeffe – two single-minded women out in all weathers, painting the great outdoors – at her best Carr has more in common with her fellow outsider Vincent van Gogh.

Emily Carr was born in Victoria, British Columbia in 1871, the second youngest of nine children of English immigrant parents who died when she was a teenager. Somehow she managed to persuade her authoritarian guardian to let her attend art schools in San Francisco and Victoria, and she even came to London in 1899. Here Carr felt her fellow students laughed at her hick ways, and indeed she laughs at them herself in the self-satirising caricatures in this show where she appears either as a prim Victorian gaping in amazement at the totem poles she saw in British Columbia, or as an eccentric colonial in a leaking hat struggling off into the woods with her brushes and paints.

Emily Carr in San Francisco, age 21 or 22, c1893. Photograph: Courtesy of the Royal BC Museum, BC Archives

The paintings of totem poles, stone birds and other carvings are not just cherished but revered in Canada as visions of a vanished culture. Like the tough-hewn, bird-beaked yet delicate columns they depict, these pictures are all solid vitality. Carr virtually lived among the indigenous people whose ancestors had made them – “the Laughing One” was her nickname – enduring mosquitoes, seasickness and several serious illnesses. Most of her pictures never found a buyer, and from 1913 to 1927 she had barely any time to paint, running a boarding house in decline, hooking rugs and breeding sheepdogs to make ends meet.

In later life she kept a monkey, a cockatoo, many dogs and parrots and transported this menagerie around the Canadian forests in a primitive shack on wheels known as the Elephant. Here she could paint day and night; a mobile Room of Her Own.

To see how far Carr came as an artist, and how it happened, you need only consult a pair of perfectly juxtaposed paintings in the opening room of this show. In 1908 Carr produces a tidy and precise Victorian watercolour of some Indian war canoes in Alert Bay. Five years later, after travelling to Paris, she paints exactly the same scene, but by now the canoes are strange purple shapes, enigmatic and resonant in a raw and excitable landscape. It is terrible to think of the long interruption that follows, but the inkling of future glory is right here: and in every sense the paintings are glorious.

Carr paints young pine trees aspiring tall but fragile in the silvery light of dawn, the air scintillating around them like St Elmo’s fire. She paints clearings in the forest where the sunlight is tinged with the deep green of the trees, which spread across the canvas like an all-over Jackson Pollock. An astonishing painting of windswept trees shows the painter’s arm moving round the scene like the wind itself, the forest branches shivering and roaring, the air made visible in a sort of spectral transparence that appears to lie both in and on top of the painting.

Windswept Trees, c1937-38 by Emily Carr. Photograph: University of Victoria Art Collection

As the painter Peter Doig remarks in the catalogue, you don’t just see Carr’s trees, you hear them too; Doig has surely taken something deep from the enigmatic power of her work.

Dulwich has more than a hundred paintings and drawings on show, but these forests are the peak – the pitch – of them all. It feels as if the great firs, oaks and spruces, the birches and maples of British Columbia are Carr’s own private totem poles. They have force of personality for her, with their uprushing trunks and dancing boughs, and their enduring, towering masses. Forests are like cities in her art, places where humanity comes together, even though there is never another person in sight.

Big Eagle, Skidigate, British Columbia, c1930. Photograph: Art Gallery of Greater Victori

Always poor – not until her 50s did Carr manage to get a work into a joint show with her fellow landscapists, the celebrated Group of Seven – she solved the problem of working in expensive oils by thinning them with petrol and painting on dirt-cheap manila paper. The effects are marvellous (if dangerously vulnerable) – breezy clouds settling on the surface like soft snow, sunlight sounding through the woods, the circumambient air lifting, moving, shining in radiating brushmarks that blur into water, undergrowth and sky.

Carr’s writings reveal a powerful sense of God in nature, but not in some mimsy pre-Raphaelite way. The divine is not in the perfection of a single dewdrop or leaf (there are no individual leaves) but in the cosmic power that gusts through the landscape. She is never afraid of the forest; she never seems afraid of anything. She suffers heart attacks, an amputated toe, extreme isolation and poverty, yet she keeps on working, drawing the surging energy around her into every picture. And when Carr finally became too ill to paint, she took up a pen instead and wrote some magnificently intelligent books about her life and that world.

The first of these, Klee Wyck, won Canada’s main literary award in 1941 and Carr was suddenly famous – four years before she died. Her own words, and not those of the critics who had paid so little attention to her, began to facilitate her fame as an artist. Canada has hugged that fame to itself, as curator Ian Dejardin tactfully puts it in his wonderful catalogue essay, but this riveting show should change all that. If you can, go and see a picture of trees that both depicts and inspires the condition of its title, namely Happiness.