What type of dart do I have?

Chrysler didn't build your car with disc brakes, not did they put an 8.75" rear axle in it. It came with 10" drum brakes front and rear and an 8.25" rear axle. Other than that your car is a very "normal" '66 Dart GT with an optional 273-4V and four speed manual transmission.
Disc brakes were a factory option starting late in the 1965 model year.
8-3/4 was available on '66 A-bodies, but not every four speed car had one.
The only other rear end available in 1966 was the 7-1/4. 8-1/4 didn't arrive until 1973.