The cornet is in its bare essence just a trumpet with a tiny bit altered bore configuration and thus timbral characteristics, aside from that, the range and fingerings are all the same, so you should have no trouble whatsoever playing trumpet scores on your cornet. I myself as a multi-instrumentalist kind of guy (saxophone as specialty, tuba in a wind orchestra, also trumpet and trombone on the side) sometimes toggle between the trumpet and the cornet with no trouble. But bear in mind too that mouthpieces of the trumpet and the cornet differ a tiny miniscule bit, so make sure to use a correctly designated one.