We critically investigate the model of a doped excitonic insulator, which has recently been invoked to explain some experimental properties of the ferromagnetic state in Ca1-xLaxB6. We demonstrate that the ground state of this model is intrinsically unstable towards the appearance of a superstructure. In addition, the model would lead to a phase separation of doped carriers into electron-enriched and neutral domains, which may be prevented by Coulomb forces only. Recent experiments indicate that a superstructure may indeed show up in this material.