You would need all of the hardware. It will work. You cannot mix soft top parts from those years, but, the entire package will fit no problem.
You will need:
Softtop with all the frame, and the frame ends with screws intact
Brackets that mount to the sport cage, and the screws for those. There is a flap that can be opened (velcro) that covers the mounting holes for the bracket.
The door surrounds. They are one piece for 2 door and 3 piece for 4 door, each side.
You will need the knurled head mounting bolts for the door surrounds. 2 for a 2 door, 3 for a 4 door, each side.
The side window. One for each side.
The rear window, the tailgate bar, and the brackets for the tub the tailgate bar mounts into.
If you have all of these pieces from the '07, it will mount to the '13.