John: There is little information on Zimmerman's service in the 1st Division. Here is what I have found to date:
Zimmerman, George R.: (Bollinger Co.) Age: 36. Elected Capt of Co B, 4th Inf Regt after enlistment in Bollinger County on 8 Jun 1861. Mustered out with company at New Madrid 26 Dec 1861.
The regiment, or at least parts of it, participated in actions at Charleston, Lucas Bend, and in the battle of Fredericktown.
I have no record for any service he may have performed after he left the Missouri State Guard.