Is it safe to put child seat on drivers seat post?
I would strongly recommend against it. I have a similarly designed seat from Yepp, and the amount of force exerted on the frame is substantial. Seat posts can shear, and would result in a bad time for everyone. 

You will also find that having your child that high up lightens the steering a lot. Mine is install in the correct position, and I have to consciously shift forward to maintain firm wheel placement; putting in on the seat post would make this even worse. 

There are some that are designed to clip to the seat post, but their design is very different: This one for example and they rest on a pre-fitted rack. 

Have you considered a crossbar seat instead?