JUNE TAYLOR, acclaimed choreographer (the June Taylor Dancers), sounded like someone with a bad head cold last week and she blamed New York for it.

"I didn't catch the cold here in sunny Miami," she said. "I caught it last week in New York with all that smog and soot."

Taylor, whose dancers made it big on "The Ed Sullivan Show" and became a regular feature of "The Jackie Gleason Show" in the '50s and '60s, was once warned that dancing might kill her. That was in 1938 and she was a 21-year-old chorus girl dancing at the Dorchester Cabaret in London. Famous director Sir Alexander Kora was arranging a screen test for her, but a strep throat got her first. In those days, before the discovery of penicillin, strep was a serious and debilitating thing. On top of it doctors found she had TB and she spent the next 2 1/2 years flat on her back in a sanitarium. It was then she was warned that "If I walked, danced or put a strain on my system I might die. I didn't want to live like that and so I went back to dancing."

Now 60, living in Miami, Fla, with her husband of 34 years, theatrical lawyer Sol Lerner, Taylor was recently hired by the Miami Dolphins to help select 24 cheerleaders from dozens of leggy candidates. "We want the cleanest, freshest, most All-American look we can get, Nice figures. Pretty faces, lively - that's today's youth," she said at the competition.

Taylor dropped out of Chicago's Hyde Park High School at the age of 14 to start her dancing career.

"It was the heavy part of the Depression," she recalled recently, "and my family needed the money." She studied with Muriel Abbott and was hired for her Chez Paree Adorables at the Chicago Chez Paree and later the Palmer House. She signed on as a chorus girl with George White's Scandals in 1938 and went from there to London where her illness intervened.

In 1955 she and her husband opened the June Taylor School of Dance on 56th and Broadway in New York. Among her students, she said, were Jane Fonda, Carol Lynley, Peter Fonda, Nina Foch and Hope Lange, who also danced on the Gleason show.

When the Gleason show moved to Florida in 1962, Taylor and Lerner decided to live there and although they tried to keep the New York school going they closed it after 12 years.

The couple own two bustling movie houses in Hallendale, Fla., and Taylor is still an active vice president for the Atlantic Foundation for Performing Arts. She teaches three jazz dancing classes a week and has worked on several TV specials.

On a recent visit to Chicago she dropped in to visit her old boss and new brother-in-law Jackie Gleason. (He married her sister, Marilyn Taylor Horwichk, in 1975.)

"He looks awfully good. He's doing beautifully. He's coming along fine," she said of the actor's recuperation from his recent heart-bypass surgery.