Redskins owner Jack Kent Cooke and his new bride Suzanne Elizabeth Martin are expecting a child early next year, Cooke said yesterday. Cooke, 74, and Martin, 31, were quietly married July 24 in the chambers of Alexandria General District Court Chief Judge Daniel Fairfax O'Flaherty. The couple spent their honeymoon at Cooke's Elmendorf Farm in Lexington, Ky., and in California.

Cooke and Martin were engaged in March and live at Far Acres estate in Middleburg. This is Cooke's third marriage and Martin's first. Cooke has two sons -- John and Ralph -- by his first marriage, which lasted 42 years. A Star Being Born? Fawn Hall, the blond-maned shredderette, is on her way to becoming a star. After all that talk about maintaining her privacy, she has signed an exclusive contract with the William Morris Agency, which, in making the announcement yesterday, said Hall has "star quality." The former National Security Council secretary/part-time model apparently does have some drawing power. When she declared her undying support for her former boss, Lt. Col. Oliver North, at the televised Iran-contra hearings, the Cable News Network reported its daytime ratings increased 200 percent.

Ron Yatter, a senior vice president of the Beverly Hills-based agency, said Hall is likely to be the subject of a book and film deal. There already is a blossoming industry in Fawn Hall look-alikes. The latest open invitation to Fawn Hall doubles is an advertisement in yesterday's Hollywood Reporter, which asks: "Do you look like Fawn Hall?" To find someone who really does, open auditions will be held in North Hollywood Friday for a part in an upcoming Bob Hope NBC special entitled "Bob Hope's Comedy Hearings." Out and About

ABC Circle Films yesterday completed its Washington shooting schedule for the upcoming 30-hour mini-series "War and Remembrance," a continuation of the previous series "The Winds of War." A broadcast date has not yet been announced. Cast members Polly Bergen, Robert Mitchum, Victoria Tennant, Hart Bochner, Peter Graves and Mike Connors were in town for several of the location shootings in the area, which included St. John's Church, the Annapolis Naval Academy Chapel, the Capitol and the Departmental Auditorium posing as Union Station. While here the film company hired 600 local extras ...

Greta Garbo's 1933 Duesenberg didn't sell for the $2 million expected, but a Houston billionaire who already has a collection of 30 Duesenbergs paid a world record $1.4 million for it at auction yesterday. Jerry Jay Moore, recently named one of the 10 richest men in the world by Forbes magazine, placed his winning bid by telephone. The auction was held in Lake George, N.Y. ...

Hospital Report: Supreme Court Justice Thurgood Marshall was discharged Tuesday from Bethesda Naval Hospital after receiving treatment for a blood clot in his right foot. He entered the hospital last Wednesday ...

Wolf Trap has learned that jazz great Oscar Peterson is at his home in Toronto recovering from the flu. There had been some concern when the usually reliable pianist did not show up for his scheduled Sunday night performance, forcing Wolf Trap to offer some 4,000 concert-goers a refund. That was only part of Wolf Trap's problems Sunday. Legendary jazz singer Ella Fitzgerald, who had also been scheduled to perform that evening, canceled earlier because of a foot infection. She was replaced by singer Carmen McRae ...

Ernest Hemingway's granddaughter, actress Mariel Hemingway, has returned home to Ketchum, Idaho, to have her first baby in the mountains where she grew up. Hemingway, 25, and her businessman husband Stephen Crisman have been married three years. She said the baby is expected on Dec. 24, Crisman's birthday. Hemingway, who recently finished filming "Superman IV," said she is taking a brief respite from the movie business to have the baby. She said she would like to spend "100 percent of the time" in their new home north of Ketchum, "but our business commitments will probably not allow that. We're going to see how much we can handle on the phone. We'll see how it works out." The couple are about to open their third restaurant ...