One of the great myths of the War of 1812 is that the British burnt Washington, DC, to the ground and destroyed all of the federal records.
First, the British burnt all of the federal buildings except the post office and the patent office and a few homes. The rest of Washington was left alone. We destroyed our own naval yard so the British would not capture the frigates and naval stores at this facility.
Second, the British did not destroy the federal papers except for a few Revolutionary War pension papers, the Library of Congress and most of the Congressional papers. Everything else was saved.
The 1790 thru 1820 census records were never kept in Washington. During these censuses, the federal marshals were the ones who conducted the censuses. The census returns were kept at each federal courthouse in each state or territory. Only the census summaries were sent to Washington.
Right before 1830, a law was passed requiring each state and territory to send their copies of the 1790 thru 1820 census records to Washington. New Jersey did not send the 1790 and 1810 records. They still may exist in a basement of one of the federal courthouses in this state.