Driving a difficult load with an Op-Amp: high capacitance, high current, high speed
The circuit design's Q1 output provides drive only in the negative-going portion of the output signal and is discontinuous.  When the signal goes positive, the current to drive the output on R6 in the positive direction cannot come from Q1, so the voltage must rise from the pull-up resistor and the RC of R1 and C2.  Meanwhile, the (much faster) op amp output is going positive to the op amp rail.  Once the R6 voltage reaches the point at which the negative op-amp input starts the op-amp drive in the opposite direction, the op-amp must come out of saturation, and drive the base and miller capacitance down to a voltage that turns on Q1.  Once again, the op-amp output will go to the rail as the base voltage lags, causing overshoot again, and the whole process starts again.  You will need a push-pull drive on this circuit so that you can drive the load in both directions and keep the op-amp out of saturation.  This will require two transistors.  You must also avoid discontinuity - in this circuit, a change in op-amp output voltage does not mean a change in circuit output unless Q1 is "on."  So, a push-pull circuit that keeps the drive amplifier output transistors in the active region.  Good luck!