Transportation Secretary Elizabeth Hanford Dole, the only woman in the Cabinet, announced yesterday that she will resign Oct. 1 to work full-time on her husband's presidential campaign.

After a 15-minute morning meeting with President Reagan, Dole told reporters that she decided Sunday that she could no longer run the department and campaign for Senate Minority Leader Robert J. Dole (R-Kan.).

Her full-time campaign work begins Oct. 1 with a 12-state swing through southern states whose primary elections are scheduled on "Super Tuesday" next March 8. She plans to operate out of the campaign's southern office in Charlotte, N.C., which is to open next month.

"This is something I have been wrestling with for some time," Dole said of her decision to resign. "There is no way I can continue to put the DOT first and get all that done."

For weeks, campaign strategists have been pushing Dole to leave the department and work full-time for her husband's candidacy, but Dole postponed the decision, saying she liked her job.

"I love my job," she said. "It's challenging, it's tough."

Sources close to the department said pressure increased on her to resign when a wave of bad publicity about aviation-safety issues began to build last month.

"She had not picked a date," a source close to the Dole campaign said. "She kept trying to escape it."

Criticism of Dole's handling of the aviation industry increased earlier this summer as airline travelers complained about service and flight delays, air traffic controllers complained about overtime and air-safety specialists began to speculate about an eroding margin of safety.

By resigning and stepping into a role of campaign wife, Dole retains the stature of a former Cabinet member while blunting criticism of her performance as DOT secretary.

"Did you ever hear anyone talk about Mode C transponders from the stump?" a Federal Aviation Administration official said, referring to a piece of airplane equipment that has provoked prolonged debate.

Dole said she made her decision last Friday and Saturday as she hopscotched through Georgia and the Carolinas on a two-day trip that combined department business with campaigning.

"Through the weekend, it came to fruition," she said. She said she discussed the decision with her older brother while in North Carolina and later with her husband before telephoning Reagan about 6 p.m. Sunday.

"If you're going to do it, this is the time," she said.

Dole's departure leaves a vacancy at the department with just 16 months left in Reagan's term. Several of Dole's top aides have left the department, and James Burnley, the department's deputy secretary, is making plans to leave.

Her possible successors include James T. Broyhill (R-N.C.), a former U.S. senator who lost his seat last November; former Pennsylvania governor Richard L. Thornburgh (R); Wendy Lee Gramm, administrator for information and regulatory affairs at the Office of Management and Budget; Patricia Goldman, a member of the National Transportation Safety Board, and former senator Mack Mattingly (R-Ga.), defeated last November.

Dole, 51, has served longer as transportation secretary than anyone in the department's 20-year history. She succeeded Drew Lewis in February 1983, before which she had worked as special assistant for public liaison at the White House.

Dole's government career spans four administrations. A Harvard-trained lawyer, she worked in the 1960s as staff assistant at the old Department of Health, Education and Welfare. Later, she worked as a legislative assistant to President Lyndon B. Johnson's consumer affairs adviser, then as executive director of the President's Commission on Consumer Interest. In 1973, she was appointed to the Federal Trade Commission.

In 1975, she married Dole and took a six-month leave of absence from the FTC to campaign for him when he ran for vice president in 1976. She resigned from the FTC in 1979 to campaign full-time for his unsuccessful 1980 presidential effort.

"I couldn't help but think back: I was gone six months at this time in 1980," Dole said yesterday.

In the transportation industry, she draws the highest praise for selling Conrail, the national freight railroad, and transferring control of National and Dulles airports to a regional authority, which is expected to be more successful at modernizing the airports.

In aviation, Dole began several efforts, ranging from writing new rules requiring airlines to report flight delays to proposing that 955 new air traffic controllers and support staff be hired.

But troubles in the aviation industry had been building for several years, and many industry executives and lawmakers said her actions were too late to help significantly.

As DOT secretary, Dole is one of the most sought-after speakers in the administration. Her husband said yesterday that she is "the greatest resource in the campaign."

In her letter to Reagan, Dole said she reached her decision to leave the Cabinet "after considerable soul-searching." She added that only a "compelling reason" could persuade her to leave her job -- "the need to elect a successor who can build on your administration's achievements."

In response, Reagan called Dole "invaluable."