In Ce-based heavy fermion materials, there is competition between the interactions which lead to a magnetically ordered arrangement of the Ce magnetic moments, and the hybridization between the local moments and conduction electrons, which quenches the local moments. Sometimes the magnetic transition can be tuned to zero temperature at a quantum critical point (QCP), where unusual properties arise due to quantum fluctuations. CeRh6Ge4 orders magnetically at a low temperature of 2.5 K, but by swapping Si for Ge, the magnetism is suppressed and eventually disappears, likely at a QCP. We propose to measure doped and undoped samples using low-energy inelastic neutron scattering, so as to probe the magnetic ground state and unusual spin fluctuations near a QCP. In particular, the scaling of the low energy scattering provides crucial information about the type of QCP.