Budget Director David A. Stockman has proposed a plan for abolishing the Department of Energy that would create a new agency for nuclear power, parcel out most other energy functions and cut only a fraction of the department's budget.

In a confidential decision memo sent to President Reagan within the last week, Stockman said his plan would save "upwards of $1.5 billion" in the 1983 fiscal year, a relatively small portion of the $13.8 billion energy budget Reagan proposed for this year. And he acknowledged that most of this money could be saved whether DOE is dismantled or not.

Of the department's remaining 18,675 jobs, Stockman said the shutdown would eliminate 4,400, nearly half of them in the Washington area. He also said he expects wide-ranging opposition to his blueprint for carving up DOE's duties and distributing them to other parts of the government, along with his effort virtually to end the department's solar energy and conservation programs.

As Stockman predicted, several Democrats in Congress, which must decide whether to ax the Cabinet department, stepped up their criticism yesterday. "This so-called dismantling is really going to save very little taxpayers' money, and it's not cutting down on the bureaucratic buildup," said Rep. Toby Moffett (D-Conn.), chairman of a House energy subcommittee. "But it's a direct hit on the idea that we ought to have something resembling balance in our energy policy."

In some ways, the Stockman plan would return the country to the days before 1977, when Jimmy Carter brought a variety of energy programs together under one roof. For example, it would abolish DOE's Economic Regulatory Administration, which has recovered millions of dollars in oil-company overcharges and other pricing violations, and leave such enforcement to the Justice Department. Stockman said opponents are sure to argue that "the rapid closeout of enforcement activities will be a de facto amnesty for wrongdoers."

The budget plan also would "establish a new Federal Nuclear Administration... for nuclear weapons, fission and fusion programs, and funding for high energy and nuclear physics." This increased emphasis on nuclear power, including both research for private industry and weapons development for the Pentagon, drew a quick response from Rep. Richard L. Ottinger (D-N.Y.). "President Reagan is using budget-cutting rhetoric to mask a Chrysler-type bailout for the nuclear industry," he said.

Stockman would shift what little remained of DOE's solar and conservation efforts to the National Science Foundation and the Department of Housing and Urban Development, even though he expects criticism that the "visibility and priority of these programs as a national concern will be diminished."

DOE's information-gathering activities would be assigned to the Commerce Department, a move Stockman says would ease the burden on private companies. But critics say the government would be forced to rely on industry's own estimates of oil and gas reserves.

Edwin L. Dale Jr., a spokesman for Stockman, said the proposal was not final. In addition, he said, "nobody ever claimed the department would achieve 15 to 16 billion dollars in spending reductions, because the two biggest items"--nuclear weapons and the strategic petroleum reserve--"are going to continue."

Stockman would let the Interior Department run the nation's strategic oil reserve, but he cautioned that "the armed services committees and their allies may attempt a return of the naval petroleum reserve to the Department of Defense." He said the State Department is likely to oppose moving emergency energy planning to the Federal Emergency Management Administration. And he predicted that every agency which is assigned new energy duties soon will be clamoring for more money.

Dick Munson, director of the Solar Lobby, said Stockman is sparing the nuclear industry from the same free-market philosophy he is using to justify an end to solar research. DOE spokesman Philip Garon countered that "the marketplace will encourage people to use solar energy on their own, but the nuclear industry is weak and requires a government presence to put it on a stronger footing."