I am only guessing but I think what you have is part of a reunion badge. Since you have that you might enjoy some of their history.
https://www.google.com/url?sa=t&rct...nia_Infantry&usg=AOvVaw2-ZP40j_tDmCptNyvOmOPp
Ok now that is simply an incredible piece of history!
The acorn represents the XIV corp badge.
It's part of a ladder badge. Search google for: civil war ladder badge
and look at pics