The doping effect of Sr and transition metals Mn, Fe, Co into the direct-gap semiconductor LaZnAsO has been investigated. Our results indicate that the single phase ZrCuSiAs-type tetragonal crystal structure is preserved in (La1-xSrx)(Zn1-xTMx)AsO (TM = Mn, Fe, Co) with the doping level up to x = 0.1. While the system remains semiconducting, doping with Sr and Mn results in ferromagnetic order with TC ~ 30K, and doping with Sr and Fe results in a spin glass like state below ~6K with a saturation moment of ~0.02 muB/Fe, an order of magnitude smaller than the ~0.4 muB/Mn of Sr and Mn doped samples. The same type of magnetic state is observed neither for (Zn,Fe) substitution without carrier doping, nor for Sr and Co doped specimens.