When Iliana Quander's fifth-grade teacher at St. Thomas Apostle Elementary School assigned her class to write a letter to the president, the Northeast Washington girl scoffed to herself, "Nobody is going to read my letter."

But the letter was read. And it won 10-year-old Iliana a coveted television appearance. She was chosen from among the thousands of children who have written to President Reagan to be one of six who will appear in an upcoming NBC television special entitled "Dear Mister President." The hour-long show, which will view the workings of government through children's eyes, is tentatively scheduled to be aired sometime in March.

Last week, Iliana, the eldest of three children of Rohulamin and Carmen Quander, lived in a room at the Georgetown Inn and had a camera crew follow her on a whirlwind tour of the city, including one visit with the president and another with the first lady.

Iliana's Jan. 17 letter caught the attention of independent producer A.C. Lyles, who said he was searching for children to appear in a program that he'd wanted to film for 10 years.

Lyles, an acquaintance of Ronald Reagan's who was allowed to review the 15,000 letters the White House receives weekly, said he was attracted to Iliana's letter because of her special request to Reagan. ". . . I am interested in getting a flag--well, at least finding out where to get one. Do you know where I could go look at one?" she wrote.

Penciled on looseleaf notebook paper, her letter was the last chosen by Lyles' staffers, as they combed through volumes of youthful scribblings. They wanted letters without political questions in them, and children from different areas of the country, Lyles said. He also looked for a Washington resident who could present a child's view of what it's like to live in this city.

Four feet tall and weighing 40 pounds, Iliana is the smallest and youngest of the six children in the special program. As the only resident of the nation's capital, she played unofficial hostess last week to the others: Christopher Joseph Turner, 12, of Springfield, Mo.; Corey DeMarco, 12, of Avis, Pa.; Scott Kendall, 13, of Huntingburg, Ind.; Kate LaPorte, 13, of Birmingham, Mich.; and Michelle Holcomb, 10, of Napa, Calif.

"I am halfway international because my mother and father are from D.C. and my grandmother is Dominican, my other grandmother is Barbadian and so on," Iliana wrote in her letter.

That was all the producer knew about the girl, who also could have mentioned that she speaks Spanish fluently and comes from a large, well-known black Catholic family that traces its presence in the Washington area back to the early 17th century.

But when Lyles saw the dainty girl in her tiny gold earrings, he exclaimed, "She's perfect. Who could look at that face and not want her to be in that show?" he recalled later.

On Friday, Iliana, a bubbly girl with long, thick pigtails who is an honor student and safety patrol at her school, got her wish when the children visited the National Museum of American History and viewed the 30-by-40-foot flag, which inspired Francis Scott Key to write the poem that became the words of the national anthem.

Lyles, who was keeping details of the program under wraps, hinted that Iliana may have gotten a special flag during her White House visit. "The president wants to keep that a secret," he said.

The children and crew were housed at the Georgetown Inn, where they could be kept handy for filming. There Iliana spent much of her leisure time chatting with friends on a telephone hung low on the bathroom wall and playing with the computer games NBC set up for the children in one of the suites.

On a shopping trip with a member of Lyles' staff each child chose an outfit, which was purchased in duplicate because of the week-long filming schedule. Iliana chose preppy attire: red pullover sweater, red plaid kilt, white blouse, red tights, and a pair of rust-colored casual shoes.

A film crew followed the children on a sightseeing tour to places that no longer impress Iliana, whose family spends many weekends at local museums, festivals and exhibits.

The filming visit to the National Zoo, she said, "was kinda like a big thing for the other kids because we have the only pandas on exhibit in this country ." At the Bureau of Engraving and Printing, Iliana's one question as she peered through the glass at the money being printed was, "How fast does the ink dry?"

Treasury Secretary Donald Regan handed each child a freshly printed dollar bill, signing them on the spot. For the cameras, Iliana sat on a huge stack of money, holding a bundle of bills, and told what she would spend it on if it were hers.

A visit with Chief Justice Warren Burger at the Supreme Court was among the other stops on the filming tour.

"She has always been calm, serious and studious like her father," said Iliana's mother, Carmen Torruella-Quander, a planner with the District's Office of Emergency Preparedness.

Iliana's parents found out about the letter after they got a call from the White House.

"At first, I thought just my letter was going to be on the show," said Iliana, giggling. "I was excited but not as excited as Mommy," she added, arching her thick eyebrows.

Catherine Mayne, Iliana's teacher at St. Apostle, described her as "a real neat kid," adding, "She's very gentle . . . very artistic. Whenever we need cards or signs, she makes them. She always dates and signs her work, very professional-like."

Among the comments of her classmates, Mayne reported that one boy asked her to say Iliana is "bigger than a lot of other people, because . . . when people tease her about her size she doesn't get mad, she just laughs back at them."

Iliana, who knits and crochets but likes better to paint and draw, said she wants to be "a doctor and an artist" when she grows up.

The Quander house on Lawrence Street in the Brookland section of Northeast Washington last week was an extraordinarily exciting place for Iliana's brother Rohulamin, 5, and sister, Fatima, 3, as well as her parents.

"We're acting like country bumpkins," Iliana's mother, who serves on several community and civic organizations, said often during the filming period. Even her father, Rohulamin, a lawyer who ran for the D.C. school board in 1979 and placed second among 12 candidates, said the experience has been thrilling.

Rohulamin Quander has already warned his daughter that her national television appearance may not "lead to anything, but she should think about the importance of it all, if it's nothing except that maybe 500 years from now someone might be able to point to a picture and say, 'Here's my great-great-grandmother with the president.' "