Does Op-Amp 741 boost the frequency of an input signal
An op-amp will not of itself boost the frequency - it amplifies voltage, not frequency.
Two possible approaches are either to use a gated oscillator or to use a phase-locked loop to change the frequency. As dog whistles are effectively a tuned circuit running at an ultrasonic frequency, the gated oscillator is probably a good bet.
Try a phase-shift CMOS circuit such as a CD4011 with delays between the gates and feedback from the third to the first gate (you need an odd number of gates to make it oscillate); the fourth gate can be a buffer to drive the output transducer. You do not need a mic for this; a pushbutton will do.