The First Lady-to-be may have reached into her closet for her Inaugural Party gown, but Joan Mondale, wife of the Vice President-elect, isn't following the leader.

Unlike Rosalynn Carter, who for sentimental reasons has decided to wear the pale blue dress she wore to her husband's inauguration ball as governor of Georgia five years ago and once since at the White House, Mondale has asked Eleanor Brenner, a New York designer whose clothes she wears frequently, to come up with special designs for the swearing in and parade on Inauguration Day and the parties that night.

Brenner, whose New York firm manufactures dresses and costumes retailing from $60 to $200, has designed two dress and coat costumes for the daytime and evening festivities on Jan. 20.

During the day Mondale will wear a two-piece dress with safari jacket styled top and pleated skirt under a nubby wool coat with stand-up neck line. Both are flame red, one of Mondale's favorite colors, according to Brenner. Millinery designer Frank Olive has come up with a small hat in fabric matching the coat.Black gloves and lowheeled pumps will be her other accessories.

For the Inaugural Party Brenner has made a dress in melon-colored hammer satin with a stand-up neck-line and pleated skirt and a white wool column-shaped coat.

"The main thing is that she doesn't want to bother with the clotes to the point that it takes her mind off what she is doing," said Brenner, who submitted sketches of the designes for Mondale's approval.

Mondale, who is perfect size 8, had bought Eleanor Brenner designs off the rack for several years before she met the designer at the opening of a Smithsonian Institution Bicentennial exhibition three years ago. Since then she has bought many of her clothes at the designer's Seventh Avenue wholesale showroom.

Brenner, a Phi Beta Kappa pre-law graduate of New York University, worked in Bloomingdale's basement "pushing racks of clothes around," until she married store executive Richard Brenner. In 1969 they opened a medium-price manufacturing business, which now also includes a line of knits and a sportswear collection.

The styles created for the Inauguration for Mondale, typical of Brenner designs, will be put on the line in other fabrics next season, according to Brenner.