Yes it will, 2007-2013 grilles are directly interchangeable.
Another option is the 2011-2012 2500HD/3500HD grille, it is a direct fit with the non-HD bumper (07.5-10 isn't). The only issue is the little strip of molding on the HDs that is on the front edge of the hood, the HD hoods have holes for the molding to mount, to mount on a non-HD you must either drill the holes, or trim the tabs off the back of the molding and use molding adhesive/tape to mount.