Using an FFT is probably counter productive. One cycle of 400 Hz is 2.5 ms so your 5 ms "tone" comprises just two cycles! It's computationally much easier to time "zero" crossings (with a modest amount of hysteresis) and that is likely to work pretty well for fairly clean signals. By the time you have to start digging into the noise to retrieve the signal things get a whole lot trickier.

Note that a 5 ms dot time represents 240 words per minute. More achievable speeds are less than 1/10^th of that. For test purposes around 5 words per minute with a Farnsworth speed of around 12 wpm is fairly typical.