In this paper, we investigate the secure transmission for differential quadrature spatial modulation (DQSM) with artificial noise (AN) in multiple-input single-output wiretap networks, where a cooperative jammer helps the secure transmission between transceivers in the presence of an eavesdropper. To evaluate the secrecy performance of the DQSM with AN in the considered wiretap networks, assuming Rayleigh fading, we derive exact and asymptotic closed-form expressions for secrecy outage probability and effective secrecy throughput under two practical scenarios, i.e., Scenario I, where the eavesdropper is passive and its channel state information (CSI) is unavailable, and Scenario II, where the eavesdropper is active and its CSI is available. Finally, numerical simulations demonstrate that increasing the transmit power of transmitter or cooperative jammer can improve the secrecy performance, but too large transmit power at the transmitter or cooperative jammer is not helpful. Moreover, increasing the number of antennas at the transmitter or cooperative jammer brings up better secrecy performance.