We investigate a state estimation problem for a linear time-invariant Gaussian system, based on a measured scalar privacy-sensitive signal. This is formulated as a Kalman filtering problem under an "event-level" differential privacy constraint, for which existing approaches, directly perturbing the measured signal, tend to degrade the estimation accuracy significantly. Here, we propose a two-stage differentially private architecture combining a finite impulse response (FIR) pre-filter with the Kalman filter. We cast the joint design of the FIR and Kalman filters as a (bilinear) optimization problem to improve the trade-off between privacy and estimation accuracy. Simulations on an epidemiological example demonstrate that the proposed method preserves estimation accuracy while ensuring event-level privacy.