Moe and Joe are going to the Smithsonian. No, not Moe and Joe's the restaurant, but Ann Miller's first tap shoes. They are a venerable 45 years old and, since she wore them off and on until eight months ago, they are, she said, "really beat up."

Frick and Frack, a pair she has had for 35 years, and Tip and Tap, mere 25-year veterans, will stay with Miller as she dances out the run of "Sugar Babies," which she has been doing since May 1979, when the show opened in San Francisco. She's been on the road with it for two years this week, although this is her first visit to Washington with the show. The durable musical, at the Warner Theatre until Nov. 18, is booked through the end of April, and may carry on through next Thanksgiving -- if Miller and costar Mickey Rooney are willing.

Miller now has written into her contact that she will not perform with anyone but Rooney. "I had to work with Joey Bishop, and Rip Taylor twice, and once with Eddie Bracken," she said with a faint air of distaste. "But we might as well face it. This show is me and Mickey."

At 65, she seems to have taken to the rigors of the road with equanimity, greeting each new town and hotel with the enthusiasm of a schoolgirl. She generally stays up until 4 a.m., wakes up at about 11 a.m., goes out to lunch and then shopping. She is so organized that she has already done all her Christmas shopping ("when I hit Neiman-Marcus in Dallas I just bought everything").

Her hotel suite is bordered with suitcases and footlockers, each marked with its contents. "There's an underwear bag, and a slacks bag, one with clothes for the show, a bag with perfumes and medicines, my business bag, and a TV bag," she explained. The "TV bag" contains flattering clothes for television interviews, such as "Adolfo or Kimberly knits in red or black." The flowing, rust-colored dress she was wearing would not be right for television, she said, because "it doesn't flatter your bottom."

At the moment she is nursing a fractured hand, wounded in a tumble down some unfamiliar steps in Memphis. It sidelined her for 10 days, and she was busy in Washington finding gloves to fit over the brace. She made no concessions to the injury once she returned to the show.

Miller still gets her special, nearly extinct long taps from the nephew of the man who sold her Moe and Joe. "The taps used now are short and have a curve," she said. "And people don't wear jingles in the heels anymore. I do a lot of heel work, so I use jingles." As for Moe and Joe, Tip and Tap, Frick and Frack and all their confreres, "I call them the Stradivarius of taps."