Is the Plymouth Duster a fastback?

It's your car. It's whatever you think it is.
That is a nice sentiment to have but not entirely reasonable or accurate.
THIS isn't exactly a woman no matter what IT claims to be:

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The Duster is classified as a fastback due to the relationship of the angle difference between the rear window and trunk lid. Look at the 73 Mustang for example...Sure, it is a hideous car but the entire window lays at barely 1 1/2 degrees from true horizontal.
The 64-66 Barracudas were true fastbacks, as were the 66-67 Chargers, All Dusters/Demons and Dart Sports and of course the specific 67-69 Barracuda.