Therefore they needed to find the unicorns, or some evidence of what had happened to them, in order to form a coherent accusation that they could take to Dumbledore. Right now all they had was "probably Quirrell is evil?" and despite all the circumstantial evidence they had, they still weren't sure what evil thing he was even doing. Killing unicorns, however, counted as evil all by itself, so that would be a good place to start, in theory.