Dryers are usually hard wired if they exceed the current draw of a standard power point.

The ID plate in your photo shows 20 amps draw, so it should not be run off a standard 10 amp power cord.

(Today they would have a special 20 amp socket and a dedicated line back to the breaker box but in those days anything over 10 amps was usually hard wired.)

I would be very wary of running it off a 10 amp socket - especially if your home has the old ceramic fuses.  Running if off a 10 amp cord would be illegal and if it causes a house fire you won't be insured.

Having got that off my chest ... it looks like a lovely machine and I think your guess of late sixties is about right. It is a great find. My grandparents moved into a furnished flat that came as part of a job package (live-in caretakers) about 1970-ish and it had a new similar washer and dryer set, the washer was a Simpson Fluid Drive with a time-line indicator. The dryer was great but the washer proved very unreliable, my Nan joked the serviceman should move into their spare bedroom.