Quantization is dividing the coefficients from the DCT transform, not the transform itself.
Note the use of both a quantizer scale code and a quantization matrix, you can vary the strength of the quantization by varying the scale code. I believe this is what we usually think of as the quantizer (qp) but the quantization matrix can still do something even if it is one. You can also simply keep the DCT coefficient matrix untouched, do the DCT transform but not use the quantization matrix at all.