As has often been pointed out, ironically this mention of "inspired Scripture" closely follows a "scriptural allusion" (to Jannes and Jambres, v. 8f) which happens not to be found in our OT canon...
As far as Jewish scripture was concerned, the early Christians were never very picky. Defining the Hebrew Bible (the Christians' OT) canon was the emerging rabbinical Judaism's business, partly against 2nd-century Christians who were only too glad to quote any Jewish text which seemed to float the Christian boat. The Christians' concern was rather to define a NT canon suitable to the emerging orthodoxy, by rejecting other Christian texts. This is not yet the point of 2 Timothy 3:16f, whose inclusive expression (all scripture, not all the Scripture) refers broadly to Jewish literature. Of course the rejection of Gnostic teachings is also an important issue in the Pastorals, but there is not yet a clear discussion of a Christian canon (this will come a little later in 2 Peter 3).
That the OT canon was still an open question among Christians is clear from the very existence of the 16th-century debate, which brought about the first dogmatical decisions on this issue (the Reformers aligning themselves on the rabbinical Hebrew canon, the Catholic council of Trent deciding for a wider canon including the "deuterocanonical" books from the Greek Septuagint tradition).