President Reagan exiled the First Dog, Lucky, to his California ranch this Thanksgiving because she was getting a little too rambunctious for the White House, according to informed sources.

One of Lucky's bothersome habits was bounding around the decorous West Wing offices. Sources said it was common to see the 65-pound, black sheepdog make a beeline for White House chief of staff Donald T. Regan's office, where she would wait for her morning doughnut.

Lucky also had pretensions to power. Once aboard the president's helicopter, Marine One, she would jump up onto the seat reserved for the president. One source describes the scene: "The president is waving to the people outside with one hand and pushing Lucky out of the way with the other."

No word yet on whether Lucky has found Rancho del Cielo to be "Dog Heaven," as her owner billed it.

SUMMITRY . . . White House officials are mulling the highlights of the Geneva summit, their biggest undertaking of the year.

Among the unexpected moments in Geneva was a request from the Rev. Jesse L. Jackson to see Reagan after Jackson had been received by Soviet leader Mikhail Gorbachev. Reagan didn't respond personally, but a senior White House official called Jackson to say that a meeting couldn't be arranged.

Jackson then proposed meeting with Secretary of State George P. Shultz. But the White House again turned him down.

TEAMWORK . . . The U.S. team in Geneva took notice when State and Defense Department officials, who have been at odds over arms control in the past, pulled together in the difficult negotiations with the Soviets on a joint statement. Assistant Defense Secretary Richard Perle and Assistant Secretary of State Rozanne Ridgway were credited with working together, and Defense Secretary Caspar W. Weinberger took note of this at a Cabinet meeting after Reagan returned, referring to Perle and Ridgway as "the odd couple" of the U.S. delegation.

STARDOM . . . Shultz earned plaudits from First Lady Nancy Reagan at a critical moment in Geneva, said one official who was present in the library of Reagan's temporary residence when the talks seemed on the verge of breaking down.

The mild-mannered secretary of state accused a Soviet official, Georgi Korniyenko, of blocking negotiations on minor accords, leading the president and Gorbachev to shake hands and promise to make some progress.

Shultz had second thoughts, fearing he had been too tough on Korniyenko. But the First Lady remarked, as they were leaving the room: "You were the star, George."

FALLOUT . . . White House officials are crowing that Geneva produced some positive results on the domestic political front. One presidential assistant said, "We've co-opted the peace issue and turned it into a positive" for Reagan, who is enjoying some of the highest public-approval ratings of his presidency. Others say that the prospect of a summit next year and a Reagan trip to Moscow in 1987 postpone the day when Reagan becomes a lame duck.

"This gives us another window of opportunity next year," for Reagan to push his domestic agenda, said a White House aide.

DECISION TIME . . . Reagan faces difficult choices on tax and spending legislation in the final weeks of the congressional session.

Aides explained last week that an endorsement of the House Ways and Means Committee tax bill was held back, in part, because the White House feared a quick approval by Reagan would anger House Republicans, some of whom are urging him to reject the legislation.

Reagan will listen to their views Tuesday at the White House, and expects to make a decision this week on how to proceed. Most aides expect a vague endorsement of the House Ways and Means bill, to keep the process moving forward, but they say that Reagan also will take into account the prospects for winning change in the Senate.

Some White House officials estimate that Senate Republicans are not anxious to deal with the issue and would rather see it die in the House.

Reagan also will face hard choices on the Gramm-Rudman-Hollings legislation. The administration is deeply split over the measure, which Reagan earlier endorsed, and White House aides say they expect Weinberger to weigh in again with his objections that the bill would slow the defense buildup.

But chief of staff Regan and his lieutenants dismiss Weinberger's concern. They say that the Pentagon would suffer even deeper cuts without the Gramm-Rudman-Holings measure, because Congress would take all deficit savings out of defense and none from domestic spending.

Said one top aide: "If you think defense is at risk now, and Gramm-Rudman is defeated or vetoed, watch out next year."