Hello Tim,
I am sorry I can't help you with the name of your ship. However, I think you are probably looking at the wrong time frame.
According to the 1850 census of Elizabeth, Jo Daviess County, the family arrived 1841-1846.
Household # 923: Ann Shimmin 50 IOM; Ellen 14 IOM; Phillip 12 IOM; Ann 9 IOM; Jane 4 Illinois; William 2 Illinois.
Also, according to the biography of Charles Bowden, husband of Ellen Shimmin, Ellen immigrated 1845. The url for Charles' biography is below.
http://www.rootsweb.com/~iljodavi/Townships/Elizabeth/Elizbios.htm
Incidentally, the same biography website gives the information that Ann Shimmin married, probably late in life, Thomas Holland.
Good luck with your research.
Lois