Sounds like the heating element has failed. If it is only 6 months old, it should still be under guarantee. Take it back to the shop where you bought it. They will probably send it back to the manufacturer for repair. Ask for a temporary replacement in the meantime.
It couldn't be the fuse if the light came on. If the fuse had gone, surely no electricity would get through for the light to come at all. I would have said the element, although it seems rather new for that to happen. Best get it checked.(Sure my husband would have said the same).