The FBI, at the request of the White House, is investigating charges by a Wisconsin doctor that Alfred Regnery, nominated by President Reagan to head the Justice Department's Office of Juvenile Justice, is "emotionally unqualified" for the job and is a "danger to the health of our children."

Regnery, who is serving in an acting capacity, provoked controversy at his confirmation hearing two weeks ago because of his plans to shift the emphasis of the office from delinquency prevention and rehabilitation toward heavier punishment for serious crime by youths.

Regnery is a former official of Young Americans for Freedom and an aide to Sen. Paul Laxalt (R-Nev.). He worked in the Justice Department's Lands and Natural Resources Division before nomination to his present post.

The Senate Judiciary Committee had been expected to approve him yesterday, but the vote was put on hold pending the outcome of the FBI investigation.

White House spokesman Anson Franklin confirmed yesterday that "the FBI is looking into the allegations right now. If any potential problem turns up, we would want to evaluate it before we go forward."

Dr. William Ylitalo, a pediatrician in Madison, Wis., touched off the investigation last week with a telegram to several senators.

Ylitalo said he warned in the telegram that Regnery, a former Madison resident, is "emotionally not qualified for that job and a danger to the health of our children."

Ylitalo has said in telephone interviews that he is forbidden by the code of medical ethics from disclosing his complaint exactly.

He did say the accusation is based on his observations of Regnery one evening in 1975 shortly after the birth of one of Regnery's four children. Ylitalo, who said he did not personally deliver the child but was present, described Regnery as "unhappy and hostile," but would not comment further.

Regnery told the Associated Press last night that he did not "really want to comment."

But he added that Ylitalo "saw me for 20 minutes eight years ago in the delivery room when one of my children was born, and we have had no contact since."

"I really do not understand what he has against me," Regnery told AP. "I understand he is an active Democrat . . . . "

Regnery said that he had given the FBI access to his medical records and expects Senate confirmation "unless they don't confirm people these days because of innuendo," AP reported.

White House sources said they expect the FBI to check any complaints about Regnery during his years in Madison. He practiced law there and also ran for district attorney in 1978.

Besides being criticized for his plans to take a harder line at the Office of Juvenile Justice, Regnery was criticized at his confirmation hearing because his car bears a bumper sticker saying, "Have You Slugged Your Kid Today?"

Regnery said the sticker had been chosen by his children as a joke and added that he had a "Nuke the Whales" poster in his office.