First, we can draw the diagram using the given description.
$\triangle ODQ$ is right angle triangle, so here we can apply Pythagoras's theorem, then we get
$OQ^{2} = OD^{2} + DQ^{2}$
$\implies OQ^{2} = 4^{2} + 3^{2} = 16 + 9 = 25$
$\implies OQ= 5$ units.
$\therefore$ The distance of point $Q$ to point $O,$ in the same units, should be $5.$
So, the correct answer is $(C).$