Hi there
I also saw your note on the next thread asking about ship records. I think I see a match for your family on the following ship:
Ship name Fides
Arrived in New Orleans Nov 20, 1854
Father Claus age (35)
Mother Margaretha age (35)
Children, Peter (11), Henry and Margaretha (twins age 7) and Claus Jr (4)
Says they were heading to Missouri so I imagine they started there before moving to Illinois.

My husbands family is also from Hannover and I found some Christening records online at Family Search.

Good luck
Lindy Bartels