Australia has a New Year's gift for the world - the first shipment of its uranium for foreign nuclear power plants.

But it is a gift the world is getting only after years of debate in and out of Australian and a national anguish unequalled since Australians wrestled their consciences in the late Sixties over the country's involvement in the Vietnam war.

The first shipment is miniscule compared with the mountains of uranium in the bleak Australian Outback.

Some 130 tons were shipped just before Christmas from the remote Queensland Mine near the town of Mary Kathleen to Brisbane, the state's steamy capital and chief port. It was the first trainload of uranium out of Mary Kathleen since 1963, and it was delayed two hours in a way symbolic of the problems surrounding the Australian uranium industry.

The uranium was put in four covered waggons marked "Danger - Radioactive" and attached without announcement to the back of a regular freight train. But groups of protestors sensed that the movement they had prevented for years had begun.

Before the slow train had travelled 50 miles of its 1,200-mile journey, a dozen protestors stood on the tracks and stopped the train. Twice more on the long journey, other groups managed to stop and hold up the train until Outback Queensland police, not noted for their gentility, removed them.

"We have achieved our objective," one protestor said. "We have drawn public attention to this conspiracy to shift uranium out of the country by stealth."

The first batch of Australian uranium is due to sail early in 1977 for the Hamburg Electricity Works in West Germany. If the conservative Australian government of Prime Minister Malcoln Fraser and the powerful Australian mining industry have their way, it will be the beginning of a huge new world trade in the valuable, controversial yellow gold - as many Australians describe their uranium.

Australian has more uranium reserves than any other country in the non-Communist world. Proven reserves of more than half a million tons is about 30 per cent of the world's known reserves. It is worth some $50 billion U.S. at current prices.

Most of it was discovered in the late 1960s in six major mining areas. By 1972, Australia had signed firm contracts with utilities and government agencies in the U.S., Japan and West Germany for 9,050 tons of uranium with deliveries to begin in 1977.

But in December 1972, the socialist government of current Australian opposition leader Gough Whitlam won power after 23 years of conservative rule.

Although Whitlam himself has never been a strong critics of uranium mining, several of his ministers were, and the whole subject was complicated for Whitlam by a factor which did concern him. The major uranium deposits found up till 1972 (and since) were in the far northwest of Australia's northern territory. It is an area known to Anglo-Saxon Australians as Arnhem land, but to the black Australians who are the only humans ever to live there, it is "Dreamtime," the most sacred of the ancient tribal lands.

Generations ago, white Australians had ignored the Aborigines and turned the area into vast cattle ranches. Mining rights were simply acquired by the whites from compliant governments which until three years ago did not even bother counting the Aborigines in the national census count.

Whitlam decided that the question of Aboriginal rights over their tribal lands had to be settled first and arrangements made for the Aboriginal tribes to get a fair share of the potentially enormous profits from the uranium mines.

He set up a judicial inquiry in 1974 under a judge, Mr. Justice Fox, to determine when and under what conditions uranium mining could start in the Dreamtime.

Before the inquiry had reported, Whitlam was unceremoniously out of office after being defeated by Fraser in parliamentary elections last December.

Fraser and his new minister for natural resources, Doug Anthony, both strongly favor allowing the Australian uranium be mined and sold to selected foreign countries. But the anti-uranium movement, led by the Australian Conservation Society, the country's chapter of Friends of the Earth and Australia's powerful left-wing trade unions, had created enough public concern over the issue to make Fraser proceed cautiously.

He said he would wait for Mr. Justice Fox's report, which ultimately was issued in November. The Fox report gave cautious approval to uranium mining and export but left for a more detailed report - due in February - the specific questions surrounding Aboriginal rights and the northern territory uranium deposits.

Just before Christmas, Fraser announced that the Mary Kathleen Mine (which the government partly owns in partnership with a public company) and a second Queensland Mining Company - Peko Ez - would be allowed to export enough uranium to complete the initial 9,050 ton's contract.

The moderate president of the Australian Council of Trade Unions, Bob Hawke, managed to wring a deal from the left-wing unions under which they agreed to lift their bans on moving uranium by rail and sea provided there would be ample public discussion before further contracts were signed.

The chances are, however, that formal debate will be minimal. Fraser's government already has ignored a move by one of its own supporters - former Cabinet Minister Don Chipp - for a free-conscience debate in the national parliament.

Uranium exporters here calculate that Australian could be earning upward of $2 billion U.S. a year from uranium exports by the early Eighties if the existing mines are given the goahead.

Significantly, the Fraser government last month passed a law which gives Aborigines the right to royalties over mining on their tribal lands - but allows the mining of existing leases, which include the bulk of the uranium mines now poised for production.

And Fraser had laid down what appears to be strict safeguards which could satisfy all but the most adamant objectors to uranium mining. They include guarantees by the purchasers that the uranium never will be used for nuclear weapons and a rule that Australian uranium will be sold only to countries which have signed the nuclear non-proliferation treaty.