Davidson was born at Stanley Park, a cattle station in Miles, Queensland, the second of two girls. Her mother committed suicide when Davidson was 11, and she was largely raised by her father's unmarried sister, Gillian. She went to a girls' boarding school in Brisbane. She received a music scholarship but did not take it up. In Brisbane she shared a house with radical biologists, and studied Zoology. Later, she went to Sydney and lived a bohemian kind of life as a member of the Push.

In the 1970s, Davidson moved to Alice Springs in an effort to work with camels for a desert trek she was planning. For two years she trained camels and learned how to survive in the harsh desert. She was peripherally involved in the Aboriginal Land Rights movement.

She has had homes in Sydney, London and India.

In 1977, she set off from Alice Springs for the west coast, with a dog and four camels, Dookie (a large male), Bub (a smaller male), Zeleika (a wild female), and Goliath (Zeleika's son). She had had no intention of writing about the journey, but eventually agreed to write an article for National Geographic Magazine. Having met the photographer Rick Smolan in Alice Springs, she insisted that he be the photographer for the journey. Rick, with whom she had an "on-again off-again" romantic relationship during the trip, drove out to meet her three times during the nine-month journey. The National Geographic article was published in 1978 and attracted so much interest that she decided to write a book about the experience. She traveled to London and lived with Doris Lessing while writing Tracks. The book won the 1980 Thomas Cook Travel Book Award and the Blind Society Award. In the early nineties Smolan published his pictures of the trip in From Alice to Ocean. It included the first interactive story-and-photo CDs made for the general public.

It has been suggested that one of the reasons Tracks was so popular, particularly with women, is that Davidson "places herself in the wilderness of her own accord, rather than as an adjunct to a man".

The majority of her work has been traveling with and studying nomadic peoples. While she is often called a social anthropologist, she has no academic qualifications and claims to be "completely self-taught". Her experiences with nomads include traveling on migration with nomads in India from 1990 to 1992. These experiences were published in Desert Places (1996).

She has studied different forms of the nomad lifestyle - including those in Australia, India, and Tibet - for a book and a documentary series. Her writing on nomads is based mainly on personal experience and she brings many of her thoughts together in "No Fixed Address", her contribution to the Quarterly Essay series. Sullivan writes about this work:

One of the questions we need to ask, if we are to have a future, she says, is "Where did we cause less damage to ourselves, to our environment, and to our animal kin?" One answer is: when we were nomadic. "It is when we settled that we became strangers in a strange land, and wandering took on the quality of banishment," she writes, and then later adds: "I shall probably be accused of romanticism."

Davidson is the subject of a song written by Irish folk singer and songwriter Mick Hanly ( lyrics). The song, Crusader, was recorded by Mary Black on her 1983 self-titled album.