  We consider the first order $q$-difference equation
\begin{equation}\tag{\dag} f(qz)^n=R(z,f), \end{equation} where $q\not=0,1$ is
a constant and $R(z,f)$ is rational in both arguments. When $|q|\not=1$, we
show that, if $(\dag)$ has a zero order transcendental meromorphic solution,
then $(\dag)$ 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 $(\dag)$ are presented.
Given that $(\dag)$ can be transformed into a difference equation, we proceed
to discuss the growth of the composite function $f(\omega(z))$, where
$\omega(z)$ is an entire function satisfying $\omega(z+1)=q\omega(z)$, and
demonstrate how the proposed difference Painlev\'e property, as discussed in
the literature, applies for $q$-difference equations.
