Another place to look for information on an immigrant’s ship is Lloyd’s Register of Ships. Lloyd’s Register can trace its origins back to the 17th century and printed its first Ship’s Register in 1764. The register was designed to provide information to underwriters and merchants on a ship’s condition. Many of the registers have been digitized by Googlebooks and The Internet Archive. On the Lloyd’s Register of Ships online is a table of years the register was printed. The years for which a digital copy exists have been hyper-linked and appear as blue on the table.
For the Brandywine Miller, I clicked on 1804 and was taken to a copy provided by Googlebooks. Searching for Brandywine directs you to the entry, which is a bit tricky to decipher as there are no headings on the columns; but they are listed at the beginning of the book.
Thus the entry can be translated as Brig Brandy Wine Miller, captain Mark Collins, single deck ship of 169 tons, built (?) in Philadelphia and had no repairs, owned by A. MacGregor, and sailed between Greenock and New York. The vessel was deemed to be of second class and built of high quality materials (E-1)