The Bell X-1A, the successor plane to Chuck Yeager's X-1, flew up to a record 90,440 ft. and 1620 mph (mach 2.44) just four years after this film was released. Not bad for a plane ordered in 1948. So planes with specs were at least on real-life drawing boards, if not actually being built at the time of this film.
Our parents and grandparents were flying some pretty hot stuff c.1950.
The plane in this film was modeled after rocket-propelled aircraft such as the Bell X-1 series and the Douglas Skyrocket. Kind of a mis-mash of the two, I'd say.