I’m sorry that I haven’t been more active here lately, but I just haven’t had the time.
I think it’s safe to assume that the craftsman who fashioned your miniature, modeled it after an historic limber, so the straked, twelve spoked wheels would definitely suggest an earlier period than our Civil War. M. Switlik’s thoughts about it probably being the model of a French limber seem sound, and his rationale also explains your model’s similarity to CW era U.S. siege carriage limbers.