LLOYD'S STEAMBOAT DIRECTORY, AND DISASTERS ON THE WESTERN WATERS
http://quod.lib.umich.edu/cgi/t/text/text-idx?c=moa&cc=m...

I'm sure this is far from a complete record but has a few.

Page 278. Seven miles below Natchez, November 21, 1846. Collision of the Sultana and Maria. Some names listed, some unknown, but no Miller.

P. 295. Queen City on the Ohio river, May 6th, 1846, German immigrants mentioned but no names.

p.291. At Natchez, May 27, 1846. Queen City. No names.

Period newspapers may be the best bet although they will be on pay sites. If your Miller (or Mueller, etc) ancestor and family were traveling steerage, I doubt they would be mentioned by name.

Good luck in your search.