E. Liflyand and F. Móricz proved that the Hausdorff operator generated by a function $ \varphi \in L^{1}(\mathbb{R}) $ is a linear operator bounded on the real Hardy space $ H^{1}(\mathbb{R}) $ by using the classical Fourier transform and the Hilbert transform, they also proved that this operator commutes with Hilbert transform. In this work, we extend these results to the context of $ q $-harmonic analysis associated with the $ q $-Rubin's operator, we introduce the $ q $-Hilbert transform on the real line, we study some of its main properties. Next, we define the $ q $-Hardy spaces $\mathbb{H}_{q}^{1}(\mathbb{R}_{q})$ by means of the $ q $-Hilbert transforms, we finally study the $ q $-Hausdorff operator and we prove the boundedness property and the commuting relation of this operator and $ q $-Hilbert transform in $ q $-Hardy spaces.