Take your Fragile Sprite Darter Egg to the Hinterlands and speak to Agnar Beastamer, but hurry, you only have 1 hour to find him before the hatchling within the egg dies.
A magnificent specimen, [your name]. If this creature survives gestation, then it'll be a healthy pet indeed!
There is one last thing I would suggest doing if you plan on following through with this--head to Aerie Peak in the Hinterlands. Speak to a dwarf there named Agnar Beastamer, he's a master animal handler and should be able to guide you in the final steps of incubation.
But hurry, [your name], this egg is fragile and will not last long without proper care.