She was devoted to the arts, to gardens and the landscape, to education and medicine, to the disabled and the underprivileged. Her name is perpetuated at places as diverse as the Melbourne Recital Centre, the Royal Botanic Gardens, the Murdoch Children's Research Institute, and the former Langwarrin Secondary College.

And it lives on in the hearts and minds of many — from the individuals whom she would greet personally at crowded public openings of her beloved garden, Cruden Farm at Langwarrin, to the mass audience that heard her declare on national television in 2008, not long before her 100th birthday: "I realise that my time must be running out, but I'm not going to waste a minute of it!"

Born five years before the start of World War I, she grew up in a modest Victorian villa in Toorak, the youngest of three daughters of Rupert and Marie Greene. Her father worked first in the wool industry, then as starter for the Victoria Racing Club.

Family finances fluctuated and her godfather underwrote her education – from the age of 11 at nearby St Catherine's School, then in the country at Clyde School, Woodend. Here her prowess at knitting woollen singlets for needy babies earned her a trip to Melbourne to tour the Children's Hospital. This was a life-changing experience that sowed the seed for her commitment to voluntary work and, eventually, philanthropy.

Aged 18, she met the influential journalist and media proprietor Keith Murdoch at a Red Cross dance in Melbourne. He had arranged their introduction upon glimpsing her photograph in his Table Talk magazine. Their age difference – he was 42 – set society tongues wagging but they were married in a matter of months.

Even though widowed only 23 years later, Dame Elisabeth always identified her loving marriage as the bedrock of her long life. Happiness gives great strength, she said. It also brought continual challenge: "I was very young, always slightly under pressure, and I had to learn to put my best foot foremost."

It showed her the enduring value of family, as she and Keith raised four children in a disciplined, loving environment – based in Melbourne, but with its heart at Cruden Farm. It taught her to work hard to strive for perfection, to appreciate quality whether in people or in beautiful antiques and works of art.

It influenced her whole attitude to life. As a very young man, Keith Murdoch had decided he should aim to be "useful in the world"; she followed his example. And it opened up opportunities. Soon after her husband was knighted in 1933, she was enlisted onto the committee of the Royal Society for the Prevention of Cruelty to Children. There followed an invitation to join the all-woman management committee of the (then) Children's Hospital.

Her direct involvement with this hospital lasted 33 years and included developing its Good Friday fundraising appeal — which has raised more than $183 million — leading its management committee (1954-65), and life governorship (from 1962). She was in charge of planning and fundraising for a sorely needed new building, and famously stared down Henry Bolte, the redoubtable premier when he objected to the proposed site in Parkville. In 1963, Queen Elizabeth II opened the new hospital and that night, bestowed on her the DBE. This followed the CBE awarded in 1961.

Her husband's death in 1952 had been a turning point. Devastated but looking to the future, she sold their city home and moved to Cruden Farm, seeing it as the tie to bind her expanding family. Each of their children had a much-used base at the 55-hectare working farm; from 1962-71 she nursed her invalid mother there. In 1975, in the face of encroaching suburban development, she secured its rezoning for rural conservation.

She devoted increasing time to voluntary work. Her "VIC 12" numberplate was a familiar sight on the road between Frankston and Melbourne, the car crammed with gifts for associates and friends – butter and cream from the farm dairy, flowers from the garden that she had begun developing in the early 1930s after design input from Edna Walling.

The 1970s and early '80s brought activity on many levels. It was not enough to give money, she believed, one had to get involved. She helped establish the Victorian Tapestry Workshop, the McClelland Gallery and Sculpture Park, the Australian Garden History Society. The chair of Melbourne University's new school of landscape architecture was named for her. She encouraged her family to set up and fund the Murdoch Institute for Research into Birth Defects, cementing her deep concern for children suffering from conditions that blighted young lives, and for their families.

She watched proudly as her son Rupert built up his media empire around the world. His buying out of the family company, Cruden Investments, allowed her to expand her philanthropic work and his sisters to build on their own tradition of giving.

Always Dame Elisabeth was conscious of her good fortune, and anxious to share it. In consequence she received innumerable letters of request, but although she donated unconditionally, she never did so without careful investigation. She lined up incognito to look through Fairlea (women's prison) before supporting a program to rehabilitate its inmates through drama. A stack of annual reports towered by her bedside, to be checked each night before embarking on whatever she really wanted to read – usually a biography or an autobiography.

Achievement followed achievement. She was the first female trustee of the National Gallery of Victoria (1968-76). She received awards for Woman of the Year (1977), Victorian of the Year (2005), Australian of the Year (2008, an honour shared with the racehorse trainer Bart Cummings). She was given the inaugural Great Australian Philanthropy Award (2003) and, in the same year, the keys of the City of Melbourne. She was appointed a Companion of the Order of Australia (1989). A star was named for her (1999), and a rose (2002). Melbourne and Monash universities bestowed honorary doctorates of laws (1982, 2008).

Accepting the 1982 doctorate, she observed: "If you expect the best of your fellow man, more often than not you will get it." Dame Elisabeth, unfailingly generous, positive and optimistic, lived her life by this dictum.

Simple and practical, she thought twice before spending money on herself, would not centrally heat her house, and grew plants from cuttings. But she never stinted on maintenance for the trees that were her garden's backbone – many of which she had planted herself – and established a system of water storages linked to a spring on the farm to safeguard the garden into the future.

She first allowed community groups to use Cruden Farm for celebrations and fund-raisers in the 1960s; by the turn of the century, special openings were occurring almost weekly (except in winter), often with many thousands in attendance. Dame Elisabeth always gave the garden free of charge, and has provided for its continued availability.

She gave her all and relished doing so, whether playing her beloved bridge, dining at the fine oak table she and Keith had purchased in 1930, hand-writing letters by a log fire in the schoolroom, circumnavigating the garden in her electric buggy with long-serving gardener and great friend Michael Morrison. She led by example, listening attentively then engaged in animated conversation, shrewd blue eyes sparkling and head tilted quizzically to one side. She made each person feel special.

She believed in the refreshment of spirit that comes with doing one's best, in the "enormous pleasure" of giving, and in the civilising influence of beauty. To her, Cruden Farm was the embodiment of beauty. She was never happier than when she was sharing it – and, by extension, herself.

Dame Elisabeth is survived by her son Rupert, daughters Anne Kantor and Janet Calvert-Jones, and by more than 70 direct descendants. Her eldest daughter, Helen Handbury, predeceased her.

Anne Latreille is a Melbourne writer.