Thanks @kuruman @Orodruin and @TSny for taking the time to engage.
It seems I was not clear in the original post, I am not trying to model the whole of the dipole that way, that I understand is not possible. Instead what I'm trying to do is model the electric dipole's behaviour on the axis...
I was trying to solve this question when I got this idea: If the electric field due to a dipole on its axis, far from the short dipole is given by (2kp)/r^3, which we can write as (k(2p/r))/r^2 here this is similar to the electric field due to a point charge, but our charge is of a special type...