President Reagan, seeking to put a woman in his Cabinet, nominated Ann Dore McLaughlin yesterday to succeed William E. Brock as secretary of labor.

McLaughlin, if confirmed, is expected to lead the administration's fight against a broad array of union-backed legislation now before Congress.

Reagan, in a Rose Garden ceremony announcing her appointment, called McLaughlin a woman of "uncommon experience and competence," and said he expects her to continue Brock's strong leadership.

Brock resigned the Cabinet post this week to head the presidential campaign of Senate Minority Leader Robert J. Dole (R-Kan.). McLaughlin would be the only woman in the Cabinet. Elizabeth Hanford Dole recently resigned as transportation secretary to work for her husband's election.

McLaughlin would be the second woman to hold the labor post. Frances Perkins held the job in the Roosevelt administration. McLaughlin yesterday quoted Perkins who, when once asked if it was a disadvantage to be a woman in the Cabinet, replied: "only when I am climbing trees."

Although she is a virtual unknown in the labor field, McLaughlin is not expected to run into serious opposition from either labor or business.

AFL-CIO President Lane Kirkland, in a statement issued by the federation, said labor had a good relationship with Brock and was looking forward to a similar relationship with McLaughlin. Top federation officials said earlier that they would not oppose McLaughlin because it was so near the end of the Reagan administration.

Despite her lack of experience in the labor area, McLaughlin is known to believe that an individual does not have to be in the labor movement to be familiar with issues of the modern workplace, particularly those that affect the growing number of women in the job market.

It was uncertain yesterday when the Senate Labor and Human Resources Committee will hold confirmation hearings. A committee spokesman said there is such a legislative backlog that it is uncertain when the panel can get to the McLaughlin nomination.

McLaughlin will have a much easier task at the Labor Department than her predecessor. Brock, who succeeded Raymond J. Donovan, spent most of his two years at the department mending fences with organized labor and other constituent groups. As a result, she is known to feel that it will not be necessary for her to spend as much time in outreach efforts.

Her biggest task will be dealing with a large list of union-backed legislation, from the minimum wage and plant closings to pension guarantees and child care. But while she is expected to oppose the AFL-CIO and other unions on most of the legislation -- she has a known distaste for government intervention -- it may not necessarily have a damaging impact on her relations with organized labor.

A lifelong Republican with strong ties to both the Nixon and Reagan administrations, McLaughlin left the Reagan administration last March after three years as undersecretary of interior. Before that, she was assistant secretary of the Treasury for public affairs under Donald T. Regan. In the Nixon administration, she was communications director for the Environmental Protection Agency. Outside of government, most of her career has been in public relations.

A top AFL-CIO official acknowledged this week that he did not expect her position to be much different than Brock's on labor's legislative agenda. As far as labor is concerned, the most important thing McLaughlin can do is to keep open channels of communication between the department and unions.