We show , through Monte Carlo simulations , that the Alcock-PaczyƄski test , as applied to quasar clustering , is a powerful tool to probe the cosmological density and equation of state parameters , \Omega _ { m 0 } , \Omega _ { x 0 } and w . By taking into account the effect of peculiar velocities upon the correlation function we obtain , for the Two-Degree Field QSO Redshift Survey ( 2QZ ) , the predicted confidence contours for the cosmological constant ( w = -1 ) and spatially flat ( \Omega _ { m 0 } + \Omega _ { x 0 } = 1 ) cases . It turns out that , for w = -1 , the test is especially sensitive to the difference \Omega _ { m 0 } - \Omega _ { \Lambda 0 } , thus being ideal to combine with CMB results . We also find out that , for the flat case , it is competitive with future supernova and galaxy number count tests , besides being complementary to them .