Elizabeth Dole supported the Equal Rights Amendment before she went to work for Ronald Reagan. But, to his credit, the first US president to oppose it does not hold that against her. President Reagan has called on Mrs. Dole to attack sex discrimination through the piecemeal means he prefers to amending the Constitution. Unless we miss our guess, her vigorous career in government says that she will not be content with window-dressing to cut the ''gender gap'' - the pollsters' finding that President Reagan rates substantially lower with women than men.
Skeptics may note that Mrs. Dole is only one of two women on the six-member White House coordinating council on women that she heads. Her clout within the Reagan team has been questioned. But the appointment is a welcome contrast with those that have seemed to signal administration retreat in protection of civil rights. Not only federal but state discrimination has been targeted br he White House. Mrs. Dole talks about having to move the states to ''corrective legislation.'' Meanwhile, her husband, Sen. Robert Dole, has recently introduced President Reagan's bill to eliminate sex-biased language from federal statutes.
As Mr. Reagan said of the measure, it is ''only one step that must be followed by many others.'' This would be acknowledged by the task forces that have studied bias in the government as well as by all the individuals who confront it in their daily lives.