The question of President Reagan's age dogged Nancy Reagan's trail into the South today on her campaign against drug abuse, but she dismissed it as a "nonissue."

"That question has been raised ever since we ran for public office," she told reporters at a suburban Atlanta shopping mall where she was launching for McDonald's Corp. a national campaign against drug use by teen-agers. The presidential age issue has been increasingly in focus since her husband debated Walter Mondale Sunday night in Louisville.

Asked about the president's comment earlier in the day that he had not looked as good on television that night because he was wearing no makeup, Mrs. Reagan said, "He never wears makeup," and then added as an afterthought, "He never has."

The first lady seemed defensive about her husband's performance in the debate as reporters here and at an earlier stop in Columbia, S.C., asked for her reaction. When one reporter noted that the president had "stumbled over words a few times," she looked slightly annoyed.

"If you're taking a poll, you can put me in Ronald Reagan's column," she said in a variation of what apparently has become her answer to that question. She added, "I thought he answered every question well and to the point and I thought he was great."

She said she had no advice for her husband on how to prepare for the second debate with Mondale on Oct. 21. "He's perfectly capable of handling himself," she said.

She denied that her trip had political tones to it. "I'm here for drugs," she said, and when reporters and camera crews burst into laughter, she put her hand to her head in dismay and scolded, "You know what I mean -- come on."

She also seemed annoyed over criticism of the luncheon she gave at the White House Tuesday to commemorate the centennial of Eleanor Roosevelt's birth.

"I was very shocked and surprised that comment was made," she said of Walter Mondale's remark that "you don't honor Eleanor Roosevelt by cozying up to racists in South Africa and dictators in Latin America. You honor her by standing up for human rights everywhere in the world."

Said Mrs. Reagan, "When you're president, you're president of all the people -- Republicans, Democrats and independents, it doesn't make any difference. If somebody deserves a tribute or recognition, you give it and Eleanor Roosevelt deserved it." She added that the Roosevelt family was "very pleased and touched" by her gesture.

In Columbia, where she visited a drug prevention program for fourth graders, she found herself confronted with still more questions. When one child asked how she would feel if Mondale defeated President Reagan, she replied, "disappointed."

"If you weren't married to the president, who would you vote for?" another youngster asked.

"I would vote for the president," she said. "I don't want to go tax, tax, spend, spend. I want to go forward."

One child wanted to know what it is like to live in the White House and whether it is much different than living in a "regular house." Mrs. Reagan told him that it's "a lot different. It's a house that's yours temporarily and you try to present it as the best house that there is. But it's a wonderful house and you can't help but feel a sense of history as long as you live there."

In Chattanooga, where she visted a residential drug treatment program called Teen Challenge, she joined a dozen born-again Christian men between the ages of 16 and 35 to hear their stories about how they kicked their drug and alcohol habits.

She said she felt her efforts to call attention to drug and alcohol problems have been successful and that where there were 2,000 parents groups when she started her campaign 2 1/2 years ago, there are now 5,000 such groups. And though she acknowledged that there can be pressures for young people, she said everyone has to realize that there are going to be problems all your life.

"Nobody ever promised us a rose garden," she said.