Doubly-fed induction generators (DFIGs) are widely used in wind turbine systems. Traditionally, they rely on the grid voltage to operate. However, the increasing penetration of renewables necessitates wind turbines that can contribute to grid stability, and grid-forming control (GFM) has emerged as an attractive solution. Traditionally, the GFM control of DFIGs has been proposed as a single-loop control of the rotor flux magnitude and orientation, while double-loop schemes based on virtual impedance or virtual admittance have been scarcely investigated. This paper analyzes the operation and small-signal stability of a virtual-impedance-based dual-loop GFM control for DFIG. The small-signal impedance-model is derived and used to analyze the system stability in case of strong and weak grid connection. Electromagnetic transient simulations on a 1.5 MW wind turbine system are presented to validate the analysis.