The Tinwhistle, as we know it today, seems to be an invention of the early 1800s. The earliest known reference to it is from 1825, one can assume that it is probably somewhat older than this.The tinplate that the original whistles were made from only became readily available in the late 1700s. As others have already pointed out, there were many antecedents to the tinwhistle made from other materials.
Dan