President Carter's plan for a separate department of education moved toward Senate passage last night.

Before a final vote was taken, Sen. Harrison A. Schmitt (R-N.M.) offered an amendment to strip out of the new department authority to take over the $350-million-a-year, 10,000-employe Department of Defense overseas school system for dependents of service personnel. He said the proposed department would "accelerate the process of bureaucratic takeover of education in this country."

However, the bill's floor manager, Abraham A. Ricicoff (D-Conn.), objected, and Schmitt's amendment lost 64 to 23.

But the Senate, responding to pleas from Indian tribes, voted 48 to 39 to romove from the new department the Bureau of Indian Affairs schools, which have 8,500 employes and a budget of $271 million a year.

Meanwhile, on a related matter, House-Senate conferees agreed late Wednesday on a bill authorizing about $10 billion a year for the next five years for federal aid to elementary and secondary schools, adult education and impact aid. The bill contains a new basic reading-writing-arithmetic skills program and will result in some cuts in the $800-million-a-year-plus impact aid program. Although authorizations are over $10 billion a year, Congress usually appropriates only half to three-fifths of the authorized amount annually.

The proposed education department would take all major education programs (except Head Start) out of the Department of Health, Education and Welfare and unite them, with some programs from other departments, in a separate Cabinet-level department of education. The president has said it would give new focus and influence to a vastly important subject, as well as a separate voice in the Cabinet.

However, conservatives have attacked a plan as likely to produce federal domination of education at all levels, while some spokesmen for unions and the poor have argued it would undermine their long-established influence on some of the programs involved or turn education programs over to narrow professionals unsympathetic to special need children like the poor and the handicapped.

A factor in the dispute over the department appears to be rivalry between the National Educaton Association and the American Federation of Teachers. The NEA supports the creation of the department, the AFT opposes it, partly, some believe, for fear the NEA would dominate the department.

Carter's original proposal was broader than the Senate bill. Carter's plan included $3 billion in child-nutition programs, but agricultural and welfare groups got two Senate and House committees to leave the child-feeding programs in the Agriculture Department.

House floor action on the measure was postponed until completion of Senate action. Some House opponents reportedly are readying floor amendments in the hope of stalling final House passage past the adjournment of Congress, or delaying it long enough so that a conference can't be completed.