In Washington where credit is not always given where credit is due, let's hear it for Nancy Reagan's wing of the White House. It is giving the Carter White House full credit for the latest renovation there: the first family beauty salon in the second-floor family quarters.

Maybe you were under the hairdryer in July 1979, when the 58,000-member National Hairdressers and Cosmetologists Association (NHCA) got the word that Rosalynn Carter had accepted the group's proposal to find donors for the redecoration of the salon. She wanted disappearing hairdryers and worktables so the room, which adjoins the family dining room, could pretend to be a sitting room. Then after Jimmy Carter's defeat, she told all to Nancy Reagan while showing her through the mansion.

Now that the project is finished, Sheila Tate, Nancy Reagan's press secretary, is saying that the project "was allowed to be finished" by the Reagans. A White House release, quoted in the NHCA Bulletin, states that "the current renovation was begun during President Carter's term." A White House photo of the finished room appeared in the NHCA November bulletin, but Mrs. Reagan's office has denied permission for it to be reprinted.

Mary Hoyt, former press secretary to Rosalynn Carter, says that though the plans were ready to go, actual work on the project never was begun.

"The cosmetologists were willing to go ahead but Mrs. Carter thought it appropriate for Mrs. Reagan to do what she wanted," says Hoyt.

Rosalynn Carter's plans for the room, which overlooks Lafayette Square, called for several wall mirrors to give a feeling of light and space since there is only one window.

But Nancy Reagan, working with first decorator Ted Graber, nixed the mirrors and opted for a more traditional approach. When all the materials were donated, they were installed by White House workmen; and the room now sports a color scheme of salmon, melon and white using $36-a-yard Haitian cotton to cover a Louis XV lounge chair, $35-a-yard Swiss-made "Les Tableaux Chinois" glazed chintz wallcoverings and draperies and a custom-made beige wool rug by the same people who did the original presidential seal rug in the early 1950s. There are two custom-modified hairdryers, a new sink, a hydraulic leather salon chair, a manicurist stool and a complete line of products by Redken Laboratories Inc. for Nancy Reagan's hair and the frequent facials she enjoys.

"It's probably the most exclusive beauty shop in the world," says former first hairdresser Evind Bjerke, who helped with Rosalynn Carter's plans but doesn't expect to see the changes her successor made.

"Very attractive and very functional," says Robin Weir who, as one of the current keepers of the first hairdo, sees the salon fairly often.

Nobody claims to have any idea of how much the "cosmetology salon," as the NHCA prefers it to be known, would cost if paid for out-of-pocket. But for the Reagan White House, the best part of it all is that none of it was paid for out of the $822,641 collected last spring from rich Republican friends to renovate the Reagan family quarters.

Some of the firms that donated furnishings and equipment are counting on more than thank-you letters on White House stationery signed by chief usher Rex Scouten -- specifically, they are counting on a tax write-off.

"I would hope so," said Thomas Walsh, manager of Clarence House in New York which donated $1,800 worth of chintz after being invited to do so bt the NHCA.