A proposal to detect the purported canted antiferromagnet order for the \(\nu=0\) quantum Hall state of graphene based on a two-terminal spin transport setup is theoretically discussed. In the presence of a magnetic field normal to the graphene plane, a dynamic and inhomogeneous texture of the N\'eel vector lying within the plane should mediate (nearly dissipationless) superfluid transport of spin angular momentum polarized along the \(z\) axis, which could serve as a strong support for the canted antiferromagnet scenario. Spin injection and detection can be achieved by coupling two spin-polarized edge channels of the \(|\nu|=2\) quantum Hall state on two opposite ends of the \(\nu=0\) region. A simple kinetic theory and Onsager reciprocity are invoked to model the spin injection and detection processes, and the transport of spin through the antiferromagnet is accounted for using the Landau-Lifshitz-Gilbert phenomenology.