  We investigate the electric dipole response of $^{34}$Na, a probable $p$-wave
one-neutron halo nucleus, lying in the "island of inversion" and having a
deformed structure. We use a semi-analytic approach to probe the dipole
response and further compare the results obtained from a post form finite-range
distorted wave Born approximation theory of Coulomb breakup. The effects of
deformation are figured out on the peak positions of the electric dipole
strength distribution which further constraint the one-neutron separation
energy of the deformed projectile and it leads to a two-dimensional scaling of
total $B(E1)$ strength with parameters: separation energy and deformation.
