The Senate Commerce Committee yesterday scheduled confirmation hearing Sept. 13 on President Carter's nomination of controversial Florida politician Donald L. Tucker to be a member of the Civil Aeronautics Board.

"In the meantime, the Subcommittee on Aviation will make a further study of his qualifications, like we do for all nominees." Commerce Chairman Warren G. Magnuson (D-Wash.) said after a closed committee meeting.

Magnuson's comments notwith standing, the investigation of Tucker apparently will be more extensive than those the committee conducts of other nominees. The President's nomination of Alfred E. Kahn to be CAB chairman moved quickly through the Senate; he was sworn in three weeks after he was nominated. The committee also is expected to schedule a hearing this month on Elizabeth E. Bailey, who President Carter nominated July 7 to be a member of the board so that she might be sworn in before the Senate takes its August recross.

Tucker's name was sent to the Senate on June 16.

The closed meeting held yesterday had been called at the request of Aviation Subcommittee chairman Howard W. Cannon (D-Nev.), who said he wanted to raise some "questions" he had about the Tucker nomination after reading the FBI background report.

The questions reportedly involve Tucker's financial statement and what is said to be his record of complicated real estate and other business transactions. He has been in the Flerida legislature since 1966, and has been speaker of the House since 1974.

Over the past few years, the Commerce Committee - which must pass on CAB and many other regulatory appointments - has given much closer serutiny to the credentials and qualifications of proposed members of regunations during the last four years. The past, and has refused to go along with a dozen Republican presidential nominations during the last four years. The committee has not yet turned down any nominations in this administration.