Hello Steve:
If Good's battery had 12 pounder field guns at Pea Ridge, they most likely were M1841 models. The problem is that this gun was considered too heavy for field service. The bronze tube along weighted 1,800 pounds and the gun carriage was a type 2 carriage weighing 1,175 pounds. This was 3,000 pounds total and the use of this gun in the field was very limited. Another problem with a 12 pounder field gun is there are only a few surviving today. My thought is perhaps they had 6 pounder field guns but Shea and Hess do not indicate this and the Official Reports are silent as to the type of guns. For your purposes, I still suggest the 6 pounder field gun as it would cost you the least of any model mentioned.
Ron Black