So your charge diverges at theta = Pi/2 ? that seems odd to me. If the disc is uniformly charged then the delta function seems to much to me.
Can't you use the delta functions most useful prop: [itex]Q(r) = \int_{\infty}^{\infty} \delta(rr')Q(r')dr'[/itex]
But i think that uniformly means that Q = rho * A (integrate constant)
