About 3 days after the PCs find it ... as long as they can maintain the proper environment for it.
What do you plan to do if one PC decides he wants to break open the egg and harvest the contents for Extra-Powerful Spell Components?
(For HotDQ, I suggested slaying the embryo inside and taking it to a taxidermist to be mounted as a footstool. With some additional work, I could magically animate it to look up when people enter the room and take a big indrawn breath, like it's going to unleash an Alpha Strike on them.)
I run a Greyhawk based campaign, with some homegrown elements, so a long timeline works best for me. A year and a half ago (real time) the characters rescued an NPC, last month they finally found out he is the heir to Furyondy lol. I like to plant plot elements early and let them mature gradually. It makes adventure hooks seem much less abrupt. It is also nice when you can have storylines intersect, and I am thinking that will be something the dragon egg will be good at.