Due to rapid progress in experimental quantum information science, a table-top test of quantum gravity may soon be possible. A promising possibility is to place two micro-solids in a spatial superposition and separable state. If, after a short time, entanglement between the micro-solids is observed then this could provide evidence of a quantum theory of gravity, assuming all other interactions can be neglected and that gravity provides a local interaction. These proposals have raised a number of questions, such as whether entanglement generation would really provide a test of quantum gravity and whether the experiments are feasible in the near term. Here, we consider whether an alternative signature of quantum gravity to entanglement could be used for a table-top test, and an alternative experimental setting. Specifically, we consider non-Gaussianity rather than entanglement and how this could be searched for in a Bose-Einstein condensate (BEC) to evidence quantum gravity. We discuss whether using non-Gaussianity and a BEC could provide any advantages to entanglement and micro-solids.