$$\rho(\overrightarrow r) = Q\delta^3 (\overrightarrow r)$$
$\overrightarrow r =$ separation vector from the origin to $\overrightarrow a$
$Q$ = the total charge of the electric dipole
Here's what I don't understand though. The total charge of the dipole is $-q + q=0$, isn't it? Therefore, my volume charge density should be zero, no?
Also, what volume are we talking about here? The question implies that we are either talking about some arbitrary volume defined when attempting to solve the problem or the volumes of the individual point charges, which are zero.