Question about electrostatics.?

Yes, it could be.

If the +ve charges on the rod is large enough, it would raise the potential of its surroundings. The potential decreases as one goes further way from the rod. Since Q carries -ve charges, it tends to go in direction towards higher potential. Hence, it will go towards P.

You may take a look from another angle from electric field lines. Most of the electric field lines originate from the +ve charged rod will terminate at the induced -ve charges on P. These field lines appear again from the induced +ve charges on the right-hand side of P, and terminate on the -ve charges on Q. Hence, Q will be pulled by these field lines towards P.

Should P be earthed, then the induced +ve charges would disappear. Q would not be drawn towards P. This is, in fact, a shielding mechanism for the +ve charges on the rod.