Zero order meromorphic solutions of q-difference equations of Malmquist type

We consider the first order q-difference equation {equation}{} f(qz)^n=R(z,f), {equation} where q=0,1 is a constant and $R(z,f)$ is rational in both arguments. When |q|=1, we show that, if () has a zero order transcendental meromorphic solution, then () reduces to a q-difference linear or Riccati equation, or to an equation that can be transformed to a q-difference Riccati equation. In the autonomous case, explicit meromorphic solutions of () are presented. Given that () can be transformed into a difference equation, we proceed to discuss the growth of the composite function f(ω(z)), where ω(z) is an entire function satisfying ω(z+1)=qω(z), and demonstrate how the proposed difference Painlev\'e property, as discussed in the literature, applies for q-difference equations.