With Egypt now firmly set on a course toward peace, President Anwar Sadat installed a new government yesterday to work with a new majority party and a new military leadership to steer the country into the future.

In Sadat's vision, Egypt is moving swiftly into a new era of peace after 30 years of war, of economic liberalism after two decades of stagnating socialism, of confronting domestic challenges after years of neglect, and of nationalism in which Egypt is putting its own interests above pan-Arab causes.

Some political observers here are skeptical whether the new government is equipped to fulfill this vision or to handle the delicate psychological and political transition Egypt faces. Though billed as a Cabinet of younger technocrats and academics, the new grouping consists mostly of men over 50 who are products of the system they have been assigned to change.

If the new government fails to achieve the reforms that admittedly are needed and does not meet popular expectations raised by peace, the disappointment could spark unrest.

As if to underline the crucial task, Sadat presided yesterday at the first meeting of the new Cabinet, formed by Prime Minister Mustapha Khalil.

The choice of Khalil was symbolic. He twice resigned from the Cabinet of the late president Gamal Abdel Nasser in policy disputes with Nasser's pro-soviet advisers, in a period of Egyptian history Sadat is doing everything possible to discred it. Later Khalil was first secretary of the Arab Socialist Union. That was the only legal party under Nasser, but Sadat had dismantled it.

The party's handsome building on the Nile has been rented out to foreign banks and the country's dominant political organization now is Sadat's new National Democratic Party.

"With the signing of the peace accords," Sadat said in a speech Monday marking the anniversary of Nasser's death, "We are beginning a new era which will witness a radical change in our internal affairs. . . Our main objective is to create a new society to achieve prosperity and to relieve the sufferings of the masses."

All this presumes that peace with Israel is an accomplished fact, and the Egyptians are behaving as if it were. The task facing the government and the party is to do something about Egypt's crushing economic problems and shoddy public services. Success, as Sadat and Khalil have acknowledged, is not assured.

Sadat said it would require a "true administrative revolution" and a comprehensive restructuring of the government - which, he said, should be carried out by "the October generation," the people who participated in the October 1973 war with Israel which Sadat said made the new era possible.

In his first public comment, the new prime minister warned against assuming that peace would automatically bring prosperity.

"I will not promise what I cannot fulfill," he said. Khalil pledged to cut expenses and improve public services, saying corruption will not be tolerated.

If he can deliver government services to the public and eliminate corruption, he will have performed feats that were beyond most of his predecessors. Khalil also must come up with a plan to develop the Sinai Peninsula, new approaches to encourage foreign investment and programs to increase agricultural production and reduce the budget deficit.

Of the 32 members of the new Cabinet, only 11 are holdovers from the last government of Prime Minister Mamdouh Salem. The changes and the rearrangement of some portfolios give indications of the way Sadat and Khalil hope to move.

The Ministry of War and War Production has been renamed the Ministry of Defense and Military Production. This key post was given to Lt. Gen. Kamal Hassan Ali, a career armor officer wounded three times in wars with Israel.Since 1975 he has not been named in the Egyptian media and his photo has not been published because he has been head of the Domestic Intelligence Service, the chief agency of internal security.

Unlike his predecessor, Gen. Mohammed Abdul Ghani Gamassi, he was not appointed deputy prime minister.

Khalil abolished the Ministry of information, saying that "state supervision of the information media has come to an end." The freedom this appears to give the press has not yet been tested, however, and Sadat in his speech Monday again cautioned newspapers to show restraint. Journalists recalled that an earlier liberalization under Sadat gave way to a crackdown after Sadat's trip to Jerusalem last November.

Another potentially significant change is the abolition of the Ministry of Local Government. The very existence of this organization symbolized the impotence of local officials who were under the thumb of Egypt's sluggish central bureaucracy. Khalil pledged that more authority will be given to provincial governors and elected local councils.

Oddly, the new Cabinet contained no foreign minister. The portfolio has been empty since Foreign Minister Ibrahim Kamel resigned three weeks ago, reportedly to protest Sadat's agreement with Begin at Camp David. Minister of State Boutros Ghali, who has been acting foreign minister, was reported remaining in his provisional post for the time being.

There is only one deputy prime minister. He is Fikri Makram Ebeid, named to handle Peoples Assembly affairs - that is, relations with parliament. He is a Coptic Christian, the first in many years to hold so high a post.