And one final note to (I believe) cover the last base of this dragon speculation: It was further stated, either by Gandalf in Bag End or later at the Council of Elrond, that even if dragonfire COULD destroy the One Ring, all the dragons are dead now anyway.
Smaug was the last of the great dragons, and he was killed some 70 years before the events of LotR.
No, it was not stated that all the dragons were dead, only that no dragon had a hot enough fire anymore. Then it was pointed out that even the fire of Ancalagon the Black (whom Eärendil slew) would not have been hot enough to melt the One Ring.
In JRRT’s “letters” he wrote that dragons persisted well into the 4th age and beyond.
Yep – it’s towards the beginning of the chapter “The Council of Elrond”… “Find it, and three rings that the Dwarf-sires possessed of old shall be returned to you, and the realm of Moria shall be yours forever.”