The new first dog, 16-pound Rex, is following in the tradition of his predecessor, 65-pound Lucky. Yesterday the King Charles spaniel pulled Nancy Reagan across the White House lawn as he headed eagerly for the presidential helicopter that would take him to Camp David for the weekend.

Rex, dressed in a body sweater, reportedly strained at his leash and barked "wildly," inciting the first lady to tell the press, "He's talking to you." President Reagan, avoiding reporters' questions about Muammar Qaddafi, pointed to Rex and said, "He's a guard dog."

It was Rex's first public trip aboard the helicopter. There was no word whether he too will be put out to pasture at the Reagans' California ranch if he continues his wild ways. Globe: Closing the Book

After more than 25 years of business, Globe Books Inc. is closing up shop. Owner Alex Roesell is negotiating the sale of the last remaining store, located at 17th and G streets NW, with Waldenbooks. Roesell says the store will retain its format, which includes an emphasis on area studies, politics and foreign languages, and he will stay on as a consultant. He decided to negotiate because, he said, "It was a very fair offer. I've been in this business a long time. It seemed an opportune time." The store will be closed for a couple of months, said Roesell, for "extensive renovations."

Mimi Figlin, regional director of Waldenbooks, declined to comment on the deal, saying only, "It's in the process." AIDS Research Benefit

Actress Elizabeth Taylor says an Arabian horse auction and an evening performance by Hollywood and Broadway stars will highlight an upcoming Scottsdale, Ariz., fundraiser for AIDS research. Taylor, chairwoman of the American Foundation for AIDS Research, announced that the fundraiser, which is expected to raise about $2 million, will be held Feb. 10. At the benefit, Taylor is slated to receive the "Woman of the Year Award" for her leadership in the fight against acquired immune deficiency syndrome. "Man of the Year" honors will go to Arabian horse breeder Eugene La Croix.

"AIDS is not going away," Taylor said at a news conference Thursday. "Though AIDS continues its relentless, savage course, we will not be defeated. We will dedicate our efforts to those courageous men, women and children with AIDS and AIDS-related conditions who are fighting for their lives."

At the "Gift to Life" auction, five to seven prized Arabians will be sold for an estimated minimum of $100,000 apiece, with tickets for the event predicted to bring in an additional $1 million. The fundraiser's glittery nighttime portion -- a performance called "That's What Friends Are for" -- will feature Hollywood and Broadway performers including Tony Award winner Donna McKechnie from "A Chorus Line," Kim Criswell and Mark Morales of "Cats," Scott Grimes from "Nine" and Fern Fitzgerald of television's "Dallas." End Notes

Placido Domingo said yesterday in a news conference at the Dexeus hospital in Barcelona that he was recovering well after a double hernia operation two days ago. "This is one performance I could do without an encore," said Domingo, 44. Domingo said he did not expect to be back on stage before March . . .

Clare Boothe Luce, former congresswoman and U.S. ambassador, was presented with the third Pioneer Achiever Award here last night at the Sewall-Belmont House. The award is given in memory of Alice Paul, founder of the National Woman's Party and author of the Equal Rights Amendment. Guest speakers at the award celebration included Robert McFarlane, former national security affairs adviser; Margaret Heckler, U.S. ambassador to Ireland; Betty Heitman, cochair of the Republican National Committee; and Helen Thomas, White House correspondent for United Press International . . .

Actor Gene Barry, star of the Broadway production of "La Cage aux Folles," was reported in stable condition yesterday after suffering from a heart attack earlier this week. Spokesman Gary Lawrence said Barry is eager to go on with the show. "It was a minor heart attack and the doctors say he has an excellent outlook for recovery," said Lawrence. Barry, 63, was admitted to St. Lukes'-Roosevelt Hospital Center in New York City on Wednesday . . .

Country singer Johnny Paycheck pleaded innocent to charges stemming from a shooting at a tavern last month. Paycheck is charged with felonious assault, carrying a concealed weapon and tampering with evidence in the Dec. 19 shooting of Larry Wise of Greenfield, Ohio. Paycheck, 47, entered the pleas Thursday during arraignment proceedings in Highland County Common Pleas Court. Paycheck's jury trial is scheduled for April 21.