
There are two other stages after egg. Hatchling and Dragon. Cracks start appearing in the egg. I think they can hatch as early as 3.5 left on their timer, but I don't remember. Once they become hatchlings, their timer starts over and they go from there. When they sprout wings(a slightly different model from their regular hatchling form) that usually means they have about 24 hours until they turn into dragons. As a side note, its the wing stage that you discover the dragon's gender.
They need a lot of attention however, so you need to get a bunch of exposure to them.