OK here are the best I could find of the old pictures. 2 interior showing the Cobra badges that should be on the dash and doors, and one of the hood. The graphics on the hood where optional but ALL 79 Cobras came with the hood scoop. The hood emblem (missing in this picture) for the Cobras was the basic running horse.
The thing throwing me off on the one your looking at is the rear spoiler. None of the ones I have seen in real life or other pictures I have had the spoiler, it could have been an option or added later.

 

Thanks for the info and pics.I will let you know if its a real cobra or not.

 

Hey found this doing a goggle search on a whim for a 81 T-top Cobra 1979 - 1981 History of the Cobra