A new Doppler radar initial orbit determination algorithm with embedded uncertainty quantification capabilities is presented. The method is based on a combination of Gauss' and Lambert's solvers. The whole process is carried out in the Differential Algebra framework, which provides the Taylor expansion of the state estimate with respect to the measurements' uncertainties. This feature makes the approach particularly suited for handling data association problems. A comparison with the Doppler integration method is performed using both simulated and real data. The proposed approach is shown to be more accurate and robust, and particularly suited for short-arc observations.