I never wondered about that since egg-laying is pretty much universal within Animalia (save most mammalians and whatever sponges, jellyfish, and other bizarro sea-dwellers do), but checking Wikipedia, dinosaur eggs appear to be pretty well-documented.
I was talking about them laying unfertilized eggs specifically. Dinosaur eggs are well-documented, but my layman googling skills can't find much about dinosaur menstruation. It seems like fish and bugs do the chicken thing of just dropping the eggs regardless of what state they're in because the individual eggs are too cheap to care about, but the most I could find about non-avian reptiles was a vague "it's complicated". Tbh I am now irate the internet isn't telling me whether snake egg farms are a viable concept, someone please help.
But that makes me wonder how mature a dragon chick is going to be. Humans are born absurdly immature and useless, birds too to a less extent, whilst reptiles usually hatch fully-featured. So labour and egg-laying could just be equivalents to get the embryo out at the same stage of development. (Given dragon lifespans I can accept 9 months to form an egg, with the time it takes for an infant to develop sensory-motor skills spent incubating, so ~2 years).
It's a good question. From an evolutionary standpoint, so long as they have a method to avoid wasting resources on unfertilized eggs, I would lean towards the standard fantasy situation of dragons hatchlings being more or less fully-featured. Nothing small enough to get away with poaching a dragon's nest is going to be strong enough to actually pierce a dragon's egg, so long nesting periods are safer than trying to care for an immature hatchling. Which is where my concerns about size come in, because I'd expect a hatchling with 1-2 years of fetal development to be at least as big as a medium-sized dog, which is...not a comfortable fit for the human womb. I guess it's possible that dragons in human form give birth to dragons in human form, but I doubt it since...
This works fine with the doujin here since wyverns at least appear precocial. The question is then whether the infant-egg can already shapeshift, and at which age it learns to control that skill.
The human transformation is a spell. According to the wiki, human magicians apparently broke the universe so badly the laws of physics can no longer properly support bodies and minds as powerful as dragons'. Staying in their natural forms for too long causes them to gradually lose their sanity, then eventually their sapience, which is what happened to wyverns and the other animalistic dragons. You can imagine all the dragon parents losing sleep over when is the right time to teach their children the human spell, and whether they messed up their kid by teaching it too late. Bonus points if they have to have a serious talk about how if you want to experiment with weed in college, that's your choice, but for goodness sake don't do all-night dragon form benders, that shit'll mess you up.