Contruct 2 currently can't work above 60fps. That means, at best, you're going to be working in about 17ms 'steps' per frame regardless of the accuracy of the input with the keyboard.
I would recommend construct classic for this task. It has an 'unlimited' mode where the exe runs as fast as possible. My computer is nowhere near top of the line and it gets about 4,000 fps using this method with a blank .cap, and I seem to recall someone mentioning getting over 10,000 fps. If you keep the content and code simple and keep all unnecessary code deactivated, hopefully it would be fast enough for you.
Construct classic also has a very high precision timer in its 'profiler' plugin. Use that and the unlimited mode together to get high precision data.
Keep in mind though that the larger the window, the more pixels the graphics card will need to redraw. Keep the window small and deactivate as much code as possible to keep the fps high.
At 5,000 fps, you're getting a precision of about 0.2 ms per step, which I hope would be adequate. If you want faster than that, you're probably going to have to use something else like raw C++.