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Take a (holomorphic) Cartan connection $E \to M$ modelled on a (complex) homogeneous space $(X,G)$, say $X=G/H$. Let $\omega$ be the Cartan connection on $E$. Every (holomorphic) vector field $v$ on $M$ is represented by a unique (holomorphic) $H$-equivariant function $f \colon E \to \mathfrak{g}/\mathfrak{h}$. Compute $df + \omega f = f' \omega$ for a unique $f' \colon E \to \mathfrak{g}/\mathfrak{h} \otimes (\mathfrak{g}/\mathfrak{h})^*$. The differential equation we need to have $v$ be an infinitesimal symmetry is that $f'$ is valued in $\mathfrak{g}$, acting as a linear map on $\mathfrak{g}/\mathfrak{h}$. So $Q=E \times^H W$ where $W=(\operatorname{End} \mathfrak{g}/\mathfrak{h})/\mathfrak{g}$.