Analogue gravity enables the laboratory study of the Hawking effect, correlated emission at the horizon. Here, we use a quantum fluid of polaritons as a setup to study the statistics of correlated emission. Dissipation in the system may quench quasi-normal modes of the horizon, thus modifying the horizon structure. We numerically compute the spectrum of spatial correlations and find a regime in which the emission is strongly enhanced while being modulated by the quasi-normal modes. The high signal-to-noise ratio we obtain makes the experimental observation of these effects possible, thus enabling the quantitative study of the influence of dissipation and of higher order corrections to the curvature on quantum emission.