No with only an 1.2 inch drop and from how you use the car you do not need adjustable arms. You should get an adjustable
panhard rod. Lowering the car causes the differential to shift in relation to the body so it is no longer centered under the car and adjustable
panhard rod will allow you to recenter it. It is not an absolute must, it is a recommendation. The other part that you probably do need are lower control arm relocation brackets. Lowering the car cause the differential to sit higher in relationship to the body which affects
suspension geometry. Take a look at you rear
control arms with the car on the ground, What you want to see is either the arms angled downward slightly from the body to the rear,(body end higher then diff end) or parallel to the ground.If that's the case then you are good, What you don't want is the the arms angled downward from the rear to the body (diff end higher then body end.) If they do then get relocation brackets. I used
J&M Extreme arms on my '10 GT with spherical bushings and currently use BMR arms on my '12 with poly bushings. i didn't notice any difference in ride quality between the two or from stock. Both worked as advertised and completely eliminated axle hop. Just about any of the aftermarket arms out there will be a significant improvement over the factory arms. Most aftermarket arms have grease fittings and require lubrication at install, after 500 miles or so, and then regular lubes going forward. So if you are installing them yourself or do your own maintenance I would get an inexpensive grease gun.
One last thing I would avoid the Ford Racing arms. If they are the ones I am thinking of they are GT500 arms which are just stock Mustang arms with stiffer bushings. Many GT500 owners I know end up replacing them.
I know this is a long post but I hope it answers your questions.