Dragons of the Third Age

[Gwaihir the Windlord]

'Think of what might have been. Dragon-fire and savage swords in Eriador, night in Rivendell.'

That was Gandalf. And in a letter to a questioner on this very matter, Tolkien;

'Dragons; they had not stopped, since they were active in far later times, closer to our own.'

This one has already been stated.

'...that there are still dragons, if not of full primeval stature.'

It seems that there are two answers. Either Scatha and Smaug bred -- Smaug was male, I don't know of a reference to the sex of Scatha -- or they were simply the only dragons to escape the battle of the War of Wrath. Other dragons were, maybe, sent out by Morgoth (to penetrate beyond Beleriand, in all probability, going to the Grey and Misty Mountains and going to ground there) before the host of the Valar attacked him unawares.

These may well have bred.

[The Hobbit, Thorin]'... and the Withered Heath, where the great Worms bred.'

And naturally this leads to another poser. Morgoth's dragons were sentient and occupied by a 'spirit', definitely a fea, the origin of which is unknown. If the offspring of these dragons were to be fea-powered as well, that is unless they simply reverted to an animal-like intelligence (nothing more that giant reptiles that flamed, then), spirits had to come from somewhere to occupy dragons. Fresh from Eru? I wouldn't have thought so. Wandering shades, shunning the Timeless Halls of Namo, would be a likely possibility for this; the only explanations that I can give on this matter.

On Smaug's apparent youngness in The Hobbit. I think it to be quite probable that in the conception of this time, Smaug was indeed written to have come as a 'dragonet' from the drake-breeding-ground of the Heath. Sharku's reference is from the post-LotR era -- which supersedes the earlier, Hobbit one without too much trouble, as nothing concrete is actually contained there. But I'd guess at that as what happened.

Of course, you can still fit it in. Smaug obviously went into hibernation in the Grey Mountains, suspended animation if you like, or at least didn't grow much comparative to what he grew in his Erebor-occupation. He was probably still very strong when he attacked Erebor, but certainly -- for whatever reason -- he waxed stronger in his lair there.