Can the Department of Justice change the date of the 2020 election?
Neither the Justice Department nor any other part of the executive branch has authority to delay elections.
Under the Constitution, only individual states and Congress have that power, and this power is not without limits. The Constitution mandates that the presidential election be held before the meeting of the Electoral College in mid-December of the election year, and congressional elections must be held before the start of the next Congress, which occurs on January 3 in each odd-numbered year.
The Constitution also mandates that a president and vice president's terms in office end on January 20 of the year following a general election. If no new president or vice president is elected by January 20, the Speaker of the House becomes acting president.