An 11-month-old girl who doctors said would have died before Christmas got a new liver and a chance to live yesterday as a result of her father's desperate plea before the nation.

In a drama that began at midnight Thursday in Salt Lake City, a team of Minnesota surgeons took a liver from the body of a 10-month-old boy killed in an auto accident and rushed it to a waiting jet.

Then, starting at 5 a.m. at the University of Minnesota Hospitals in Minneapolis, they transplanted it into gravely ill Jamie Fiske and announced, "We're very pleased. With luck, she should do well."

Jamie is the little girl doctors said could not live until Christmas, and might die before Thanksgiving, without the transplant. The daughter of Charles and Marilyn Fiske of Bridgewater, Mass., she had been waiting for one since September at the Minneapolis hospital, one of the country's leading transplant centers.

She was born last Thanksgiving with unformed bile ducts. Two operations in Boston failed to repair them. The bile made in her liver was poisoning her body, and her blood would not clot. She needed a liver from a child weighing 15 to no more than 17 pounds, hopefully one of matching blood type. None was forthcoming.

Last week her father went to New York and spoke to 400 doctors at the annual meeting of the American Academy of Pediatrics. "Keep your eyes and ears open for the possibility of a donor for my daughter," he begged.

At the University of Utah Medical Center Thursday a baby was brought in from an auto accident. He was brain dead. His parents had seen Fiske's plea on television.

They told doctors, "Our boy is going to die. Could his liver help the child in Minneapolis?"

The Utah doctors telephoned Dr. John Najarian, University of Minnesota Hospitals surgery chief. Jamie and the Utah child both had Type O blood. Najarian leased a jet and dispatched Drs. Nancy Ascher and David Sutherland to remove the Utah child's liver in a three-hour operation.

Yesterday morning, Najarian and Ascher began six hours of labor to reconnect the softball-sized organ.

"It's the most difficult transplant operation, especially in a baby," said Najarian, a surgeon known as a skilled kidney transplanter.

The soft, fragile liver had to be reattached at four places: two arteries and two veins, all slim, delicate and easily torn. Then Najarian, Ascher and assistants had to connect the girl's gall bladder, tucked just beneath the liver, to her small intestine, to make an ingenious way for the liver bile to reach the intestines.

In short, Najarian said, "You have to do five different things, each of them very demanding and each tucked in places difficult to get at, not out in the open.

"Now," he said, "we're over the biggest hump."

The new organ still could be rejected, though in the past two years an anti-rejection drug called cyclosporine has made kidney, heart and liver transplants more successful.

Five years ago Jamie's chances would have been called slim, however skillful the surgery. Two years ago Dr. Thomas Starzl, then at the University of Colorado, now at Pittsburgh University, started using cyclosporine in liver transplants. Eighty percent of his patients have lived at least a year, and at least 40 percent, he estimated, will survive at least five years.

For Jamie, Najarian said, there will be a long critical period.

But, he said, the new liver started to function while Jamie was still on the operating table, and, he added, Jamie has a good chance of living a normal life.

"I have told her parents" this, he said. "They were overwhelmed."

Also kept informed during yesterday's surgery was Nancy Reagan, whose prayers, a White House aide said, "are with the family." She had telephoned Jamie's mother last week, and the aide said they "cried their way" through a five-minute conversation.

The name of the dead boy who provided the liver was not disclosed.

"At this point," a Utah hospital spokesman said, "I have to respect the privacy of the parents, who must be going through quite an ordeal right now."

A Minnesota hospital spokesman said Massachusetts Blue Cross-Blue Shield has promised to pay the $60,000 to $70,000 that Jamie's care is expected to cost. The University of Minnesota transplant service probably will pay the $8,000 it cost to lease a Lear jet for the liver, the spokesman said.

The luckiest part of the story, of course, was the gift of the liver. Liver, kidney and heart grafts must usually come from persons fatally injured in accidents, who die quickly so their bodies are otherwise healthy.

Two children are waiting for livers at the Minnesota hospital. Forty-nine adults and children are waiting at the University of Pittsburgh.

"Since our liver program began in 1981," a Pittsburgh spokesman said, "32 adults and 16 children have died waiting."