Basically, there would be this dragon egg that you could find in a randomly chosen spot in skyrim (perhapse a cave that would be picked by radiant story). This egg would obviously be guarded by a dragon that the player would have to kill. After slaying the beast, the player would then be able to approach the egg with whatever intent they wish, weather that be to examine it, or destroy it. However, as they get within a few feet of the egg, it suddenly starts to hatch, and a small baby dragon emerges. ( it would only be small compared to its advlt counterpart; compared to the player, it would probably be about half their size give or take)
Now, from here the player can kill the dragon, seeing it as a threat. They could continue their approach and perhaps give it a piece of food or whatever baby dragons eat, thus befriending it. Or they could simply stay back and observe it until they decide what to do with it.
If you befriend it, then after a few weeks of caring for it, it could aid you in battle in different ways. Perhapse there could be some self given quests that you can go on in order to teach your dragon how to do different things like maybe how to fly so it can aid you better in a fight with another dragon.
Oppinions? comments? suggestions? feedback?