The one thing you can say is that if your test environment can handle 1000 users/second with a response time < 1s, then your production environment can handle at least the same.
You can't do a straight linear extrapolation unless every part of the production is x times as powerful as the test system. That doesn't just mean double the memory and double the CPU speed. It also means double the BUS limits, double the disk access speed, double the network capacity, double the task switching speed... and possibly more depending on precisely what resources the system uses.
The prod system may have limits that aren't reached in the test system, such as request limits, queue limits, and so forth. Those can be hard limits based on the operating system, or they can be configurable but cause other issues if they are changed from the default.
The only thing I would say for certain is that if the test environment handles 1000 users/second with response time < 1s, the production environment will handle more than that. How many more will depend on too many variables to be able to give a confident estimate.