We know that the Sceptre of Annúminas had its origins as the rod of the Lords of Andúnië in Númenor. The first of those Lords, Valandil, achieved the title at some point in the seventh or eighth century of the Second Age, and so the Sceptre probably dated back to that time. It is never stated explicitly, however, that the Sceptre brought to Middle-earth by Elendil was the original rod of Andúnië. Given that no comment is made on the matter, it is probably fair to assume that it was indeed the original, but conceivably the old Sceptre might have been replaced over its long history in Númenor.