The long trip ended at Dulles Airport yesterday for Linh Brooks, the 12-year-old daughter of a Vietnamese woman and an American man. But her real odyssey, a new life in a strange new land, had just begun.

And it began with an American ritual -- the press conference. Before a row of television cameras, Linh was reunited with her mother and her sister and brother, who live in Washington's melting-pot neighborhood, Adams Morgan. She had not seen them since April 1980, when they fled Saigon on a boat bound for Thailand. Linh had been staying with her aunt, and there was no time for her to join the hastily planned escape.

"I am very happy," Linh's mother, Cao Thi Nhan, told the pack of reporters who met the family at the gate. "What else is there to say?" Linh, who had been traveling for more than two days, looked dazed and scared as she faced the press.

Reporters asked how she liked the American pancakes she had been served on the United Airlines flight from Los Angeles and how she liked the movie -- "Rocky III." Linh speaks no English and the questions were put to her through an interpreter. But she couldn't answer and just gazed into the crowd of strangers, holding the hand of her 11-year-old sister.

She was one of 11 children of Vietnamese-American parentage who arrived in the United States Sunday, the largest such group to leave Vietnam in seven years. Thousands more Amerasian children are expected to follow, their emigration arranged by refugee assistance groups. Congress last Friday approved a bill granting U.S. citizenship to children in Vietnam who can prove American parentage.

They are known among the Vietnamese as bui doi (dust children) because many, denied housing, ration cards and schooling, must earn their way in the streets, sometimes turning to crime and prostitution. The number of children in Vietnam, Thailand, Japan, South Korea and other Asian countries fathered by Americans has been estimated at from 80,000 to 250,000.

Linh's father, Kenneth Brooks, who was a civilian aircraft mechanic in Saigon, where he met and married Linh's mother in 1968, was absent yesterday. He lives in Chicago and sends money to the family regularly, his wife said. She works in the employes cafeteria at the Shoreham Hotel.

The only member of the family who seemed at ease with all the attention yesterday was Linh's brother, a smiling 13-year-old named Keit, who wore a pair of binoculars around his neck and held a Polaroid camera.

"I feel happy, I feel very happy," he said into the microphones. He was asked if he thought his sister would like her new home. "I think she like it here . . . . Why? Because it's a very beautiful place over here."

He held up the color picture he had snapped of the sister he had not seen in more than two years. One photographer immediately asked if he could borrow the snapshot, but an official with the International Rescue Committee intervened, and the boy was able to keep his picture.

Kiet and his sister Lan attend Bancroft Elementary School where, rescue officials said, Linh will probably also go to school. The family traveled from Thailand to Washington in May 1980. They live in a one-bedroom apartment.

A small crowd gathered to watch the media greeting of Linh Brooks. A grandmother from New Jersey named Doris Kilmer, who was at the airport meeting her son-in-law, said her heart went out to the 12-year-old from Vietnam. "She must be so scared . . . ."

The press conference soon ended, with Linh's mother pleading through an interpreter that her daughter was tired. International Rescue Committee officials whisked Linh and her family away, past the gift shop selling such items as Smurfs and Muppets dolls, "Runners' radios" and checkbook calculators, the first of what will surely seem a never ending array of baffling wares the girl will find in America.