Detecting frequency when frequency is not sufficiently greater than baud rate
You should read https://en.wikipedia.org/wiki/Minimum-shift_keying.  The minimum frequency distance between two FSK tones is half the baud rate.  But even at 1X the baud rate, the tones look blurred together in the spectrum.  Note that, without any pulse shaping, the bandwidth of each tone is effectively the baud rate.  This is related to the implicit rectangular window that is applied by the digital modulation.  So you have two tones that each have a width of the baud rate.  When the separation between them is the baud rate, the left sided half bandwidth of the high tone combines with the right-sided bandwidth of the low tone and you get one big blob.  If you were to pulse shape the signal in the phase domain, the single-tone bandwidth would be reduced and you would get more visual separation between the tones.

Demodulation for MSK is usually done in the phase domain, not the frequency domain for this reason.  If you plot the unwrapped phase of the signal you would see the phase sloping up for the high tone and sloping down for the low tone (assuming you're using a complex analytical form of the signal). You can demodulate the signal in the phase domain by using a filtered differentiator on the phase of the baseband signal which is basically an FM demod which turns an FSK signal into a BPSK signal.  You can also use a Phase locked loop (which is another form of FM demod).