West Coast Cobras used to use similar outside door handles on their stretched and "re-proportioned" replicas, but your car definitely is not shaped like a West Coast.
The stretched wheelbase, Chevy engine and the shape of the body - particularly the way the line of the body "turns upward" from the doors forward - reminds me more of one of the Corvette-based kits like the Cobrette. There were a few different ones out there, but that is my guess. The firewall area is pretty distinctive, and more pics as suggested above will help narrow it down.
Here's a link to a photo of a Vette-based Cobrette for comparison. Note the shape of the body forward of the windshield.
On the other hand, the shape of the nose and the hood scoop do look a bit like a West Coast, while rear fenders are clearly different. West Coast kits have a very large, rounded rear fender shape and were generally set up for big block ford (385 series) engines. Here's a look at a West Coast - note the differences in body shape.
