WE WILL spare you any of those awkwardly qualified, impersonal-sounding "first woman" references to President Reagan's latest Cabinet nomination. On all grounds, Elizabeth Hanford Dole is a strong choice for what has fast developed into a more demanding, complicated and important public responsibility as secretary of transporta- tion. Mrs. Dole is an accomplished and skilled member of the administration already, and her legal, managerial, political and government experience should stand her in good stead as head of one of the largest and most diverse of the federal agencies.

While transportation traditionally has not been regarded as one of the front-rank positions in a president's Cabinet, time is changing that: the jurisdiction and responsibilities of this department, as well as the immediate tasks facing the next secretary, touch the daily lives of every American and involve, in one way or another, 20 percent of the gross national product. Among the issues that should command close oversight are these:

Highways, bridges and mass transit. Success of the just-enacted nickel-a-gallon increase in the gasoline tax and the complicated provisions in this legislation will require constant supervision to ensure the proper use of the new money that will be there to spend, money that can turn into the makings of bid-rigging, pork-barreling and just plain waste. If improvement of ground transportation is the objective, the next secretary also will have to continue to prevent the Office of Management and Budget from stockpiling revenues in the highway trust fund for general financial cosmetic reasons.

* Air traffic control. The post-PATCO war rebuilding is far from over, and it may be the toughest of all the personnel jobs, from the training and deployment of controllers to the reshaping of management and the replacement of enormously expensive computers for the whole system.

* Auto safety. A less-than-stellar record in strengthening automobile safety regulations invites new initiatives.

* Shipping. The Shipping Act, which would have allowed shipping firms exemptions from antitrust laws for certain agreements with shipping cartels, died in the Senate last year, as it should have; but this provision and other unresolved matters merit administration thought and proposals.

* Conrail. Here, too, a firm adminstrative hand will be needed to oversee the changes in store for railroads.

* Local matters. Union Station's revival, Metro's construction and operations and National and Dulles airport policies will continue to be matters of top importance to the national capital area.

With all this to be done, and with an able nominee ready to take it on, there is good reason for the Senate to confirm the nomination of Mrs. Dole swiftly and enthusiastically.