Okay ... Making an April Fool's joke into a real character is certainly creative and I've seen some really good suggestions in this thread.
To answer this 'canonically':
My source is the _really good_ ED Dragons sourcebook, as it has a big chapter about the life cycle of dragons.
Eggs are generally cared for by great dragons, and the hatchlings will have the form of the foster parent instead of the biological parent. So, if a western dragon gave her eggs to Lung to take care of, her hatchlings would become eastern dragons. Asking a great dragon to take care of eggs is also a bit like a job application, the female needs to persuade the great dragon of her and her offspring's future qualities. After the eggs are placed in the foster parent's care, the biological parent will most likely never see them again. For all intents and purposes, the great dragon is father or mother to the eggs under his care. It's even hinted that they cannot even hatch without a great dragon nurturing them.
It is also the most sacred duty for all dragonkind (not surprisingly, since they are very few and it's very similar in human culture, too).
Eggs grow during incubation from around 1 foot size to about 4 feet height just before hatching. New born dragons are between 2 and 4m long, with legs and wings (no forelimbs in case of western dragons!), with a barbed tail. Notice the similarity to a wyvern yet?

Anyways, during the incubation, which can take about a century, the dragon actually teaches the hatchlings via dragonspeech. This is not yet formally education, but rather low level telepathy to make the hatchlings receptive to the one they receive after hatching. They are being told who their guardian is just after emerging from the egg, at which point the formal relationship begins.
They learn basics like flying, hunting and surviving rather fast in their first years and learn to use their magic at around 20 years. At ~50 years they learn about draconic history as well as the other people living in the world around them. Obviously, this takes place in rather secluded places and may not be as viable in the sixth world, where knowledge is even more power than in a sparsely populated 4th world. They usually keep in a 4 day walking radius (I'd say around 80-120km) around the lair where they hatched but are intensely watched by their guardian. Outsiders are discouraged to enter such areas with measures ranging from subtle to extreme, and the guardian is always nearby when they fly out to hunt (seems unlikely in the sixth world, but maybe there hasn't been a new hatching yet. The greats all seem rather preoccupied with their schemes).
So, pertaining to the teenager idea: Hatchlings usually do not experience raging hormones ... that is, until they're about 200 years old.
Which is when
nothing special at all happens. At least that's what the dragons say.
In truth it is strongly hinted that they become almost feral during the next hundred years or so, and that those are what people call wyverns (at least in the case of western dragons). They are vicious hunters, they grow fast and almost to their full size during that period and they are smart and deadly. However, they are not very cunning and about 2/3 of all dragons die during that phase of their life. Even their guardians and other dragons avoid them during that time, as they still tend to flock together despite being territorial. I guess they're staying together with the other hatchlings from their clutch.
They are also unable to use their magic during that period (hormones really suck, huh?)
When they grow out of it, they physically enter astral space and weave a magic cocoon and their body changes to its final form over the course of 5-10 years. It's not said specifically, but I reckon that all dragons share the same hatchling form until this phase. When they emerge from the cocoon, they are about 300 years old +100 years of being in an egg, and take their own name, which is the point where they introduce themselves to draconic society and claim their lair and can start procreating. They usually remain in good contact with their guardian, but there are no lingering debts from being brought up. If they come up it's over the course of their adult lives and they may become a sort of vassal to a great (or just an older) dragon, e.g. in exchange for further teaching, or because they want to live in an area claimed by another dragon (for various reasons)
tl;dr version:
Dragon teenagers are a bit older than 14, they are vicious monsters that will sting you to death and the youngest western dragon is a full blown adult who is several centuries old and in full command of his powers (such as they may be).
But that would be, in the context of your campaign, BORING

Hatchlings on the other hand are rather communicative, while certainly not unschooled. They would also be highly sought after if they go missing, because ... well, with a dozen eggs taking a hundred years to hatch (and some of those even die unhatched) and a further two thirds dying in adolescence ... Let's just say, dragon population is not the most stable.