Ian Eaton is 7 1/2 months old and "21 pounds of solid, breast-fed muscle," according to his proud mother. He has become something of a media celebrity of late, but after the fuss settles down he may grow up to be a fireman like her.

Ian has been spending more time in firehouses than most children his age - an average of about an hour per day, divided into two half-hour visits, on the days when his mother, Linda Eaton, is working her round-the-clock shift at the central fire station in Iowa City. He was in Washington yesterday, with his mother, raising funds for a legal battle to secure his right to have lunch (breast-fed) in the fire station.

He also renewed his acquaintance with Midge Costanza, whom he had met earlier at home when she came out to speak at the University of Iowa and, while in town, was won over to his mother's cause. At their first meeting, Costanza recalled, he had needed something to play with and she had let him borrow her keys.

"Actually, men are all alike," she said. "He took my keys and asked me what time I would be through. I think he's a little young for me, but Amy [Carter] has a taste for younger men."

Originally, Costanza had not wanted to be involved in the widely publicized Eaton case because, she said, "the headlines gave the impression that she was breast-feeding the baby in the middle of the firehouse with 30 firemen watching."

Actually, the feeding takes place in the women's locker room with Linda Eaton shares with several policewomen. At first, the fire cheif objected on the grounds that she would be slowed down in responding to an alarm, but alarms have come in twice while Ian was having lunch and there was no problem. She simply handed him to the babysitter, and left.

"If I'm feeding Ian," she said, "it takes me about 10 seconds to get to the truck. The first time an alarm came in during a feeding, I was the second firefighter to reach the truck. I was worried that he might get psychological problems, associating an alarm with the end of feeding, but that's not happening."

Eaton is 26 years old, 5-feet-9 inches tall and a muscular 145 lbs. Her chest-nut-brown hair is long and free in the style of a liberated woman, and she wears a silver pin with the initials "F.D." (for "Fire Department") on her denim jacket. "They told us we couldn't wear them on our uniforms," she observes. "Some of the men have them, too, but they want everybody to look alike."

To become the first women fire-fighter in Iowa City, she had to pass tests which included carrying a 180-pound man 100 feet using the fireman's lift, dragging him the same distance with the fireman's drag, running a mile, doing pushups and situps and climbing almost to the top of a 100-foot aerial ladder. She made all-state honorable mention as a guard with her high-school basketball team, and she notes matter-of-fact pride that she is "bigger than some of the men in the department."

In a complicated legal battle, which will be settled ultimately by the Iowa Civil Rights Commission, Eaton has won a temporary injunction that allows her to feed Ian at the firehouse twice a day for not more than 35 minutes per visit. In a flanking effort, the city council and fire chief have now restricted the traditional right of families to visit firefighters while they are working - but this restriction does not affect Eaton, who is protected by the court injunction.

So far, court costs have amounted to $4,500 for Eaton, making Ian's meals considerably more expensive than they would be if he had them out of a bottle. "They're using tax money to fight against Linda Eaton's civil rights," said Marge Penney of the Iowa City chapter of the National Organization for Women and the chair of the Linda Eaton Legal Fund.

Before NOW offered help, Eaton (who is not a NOW member) was fighting on her own. "I am a single parent," she told guests at last night's fund-raiser. "Ian's father has been very supportive in private, but in this battle I stand alone." While she spoke, Costanza volunteered to hold Ian. "In the event that I run for public office," she told the infant, "you will be the first baby I kiss." CAPTION: Picture, Ian and Linda Eaton; AP