National Archives arrival record for George Dute and family for the Brig Bremen Packet, arriving in New York 9/1/1834 from Bremen, courtesy of Barbara Dute Hart and Karen Krugman. George is 34, and his occupation is hard to read but it might be farmer:

George's wife and son are on another page; the wife Anna Catherine is not mentioned by name here but the last name looks like it's preceded by "Mrs", and the age looks like 29 which is correct. Casper is 7:


On the same ship were Casper's future wife Mary Heidenreich and her family. The complete passenger list is found below, located by Kate Fricker, and the following transcription of some of it is by Ted Reising:

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Brig 'Bremen Packet' arrived NY Sept. 1, 1834:
  Some of the passengers were:  (not necessarily in manifest order; 
most of the 'heads' of families were recorded on this manifest's first 
page, and their families recorded on the manifest's second page.)
=========
HERWIG,  Jacob 37 [c1797] miller [ b.1795  d.2 March 1873]
Anna 39 [c1795] [d.1851]
Barbara 11 [c1823] [she later m.(1840) to passenger Henry HILDEBRANDT]
Christ  "male"[actually should be Christina, female]  8 [c1826][she 
later m: Adam BAUMHARDT].
Jacob [Jr.] 6 [c1828][he later drowned, 1863, with his wife and all 5 
children in Beaver Creek, west Lorain.]
==========
YUNGMAN, Andreas [Andrew] 28 [c1806] mason
and 
YUNGMAN, Mrs. 24 [c1810][prob. Hannah]
[in 1850 Blk. Rvr. Twp., they lived directly next to the HERWIGs]
==========
DUTE, George 34 [c1800] farmer, [George, 1800-1875] 
and 
DUTE, Mrs. 29 [c1805]  [prob. Catherine A., 1804-1868]
DUTE, Casper 7 [c1827]  [Casper, 1827-1900] [later m: Mary HEIDENREICH 
who was also passenger on this ship.]
==========
HILDEBRANDT, David  47 [c1789] carpenter [b.1785 d.1856]
and (in order as recorded)
HILDEBRANDT, Anna 16? [c1818]
HILDEBRANDT, Bernhard 19 [c1815] [d.1871]
HILDEBRANDT, Zacharius?  13 [c1821]
HILDEBRANDT, Mrs. 48 [c1786]  [prob. Katherine "Gerderuth" 1783-1855 ]
HILDEBRANDT, Miss 10 [c1824]
HILDEBRANDT, Miss 7? [c1827]
HILDEBRANDT, Zacharius?  25 [c1809]
HILDEBRANDT,  Henry 22 [c1812] [he later m.(1840) to passenger Barb. 
HERWIG]
==========
HEIDENREICH, Heinr. 40 [c1794] farmer [Johann Heinrich 1795-1879]
and
HEIDENREICH, Mrs. 44 [c1790] [prob. Katherine 1788-1856]
HEIDENREICH, Kath. 11 [c1823]
HEIDENREICH, Anna 8 [c1826] 
HEIDENREICH,  Mary (f) 5 [c1829]
 [Kath. later m. Henry HOLZHAUER; Anna E. m. Val. SELIG and moved to 
Kansas; Mary m. Casper DUTE who was also passenger on this ship.]
==========
another passenger with possible Lorain Co. connection:
LUTZ, Andreas  23 [c1811] carpenter
==========
and another whose name was crossed off:
Eliz. GERLACH  (no age)

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A few more transcriptions from the passenger list, done by Deb Bromley:

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Ship "Bremen Packet" arrived NY from Bremen on Sep 1, 1834.  On board is:

  Casper Dute age 7 with his mother
  Mrs. Dute age 29 (which would be Anna Katharine Muller)

  Mary Heidenreich, age 5 (who married Casper)
  Anna Heidenreich, age 8 (who married Johannes Holtzhauer)
  Katherine Heidenreich, age 11
  Mrs. Heidenreich, age 44 (Anna Catharine Hilt?)

  Jacob Muller, age 54
  Mrs. Muller, age 34
  John Muller, age 11
  George Muller, age 5
  Jacob Muller, age 6

  Also on this ship looks like Herwitz, Hildebrandt, Agatz, and Schuholtz families.