if by connie you mean the 24th century Connie (TNG refit), then I think that just higher armor and more phaser power would do. maybe along the lines of the armor on the Ambassador (that's a King's gift for a Connie) and the phasers on DS9, or those in the Excelsior.
just try to keep the connie smooth (texture-wise) and thinking of it as an explorer, not a warship. just give her the chance to survive against two or three dominion fighters.