How does Julia not age?

She has been in stasis. In stasis it is commonly assumed one does not age.

Wikipedia has a great page on this:

A stasis field is a region where a stasis process is in effect. Stasis fields in fictional settings often have several common characteristics. These include infinite or near-infinite rigidity, making them "unbreakable objects", and a perfect or nearly-perfect reflective surface. Most science fiction plots rely on a physical device to establish this region. When the device is deactivated, the stasis field collapses; that is, the stasis effect ends. Time is often suspended in stasis fields. Such fields will thus have the additional property of protecting non-living materials from deterioration. This time dilation can be, from an in-universe perspective, absolute, so that something thrown into the field, has the field triggered, and after any length of time reactivated, would fly out as if nothing had happened. Storylines using such fields often have materials as well as living beings surviving thousands or millions of years beyond their normal lifetimes. This property also allows for such plot devices as booby traps, containing, for instance, a nuclear bomb. Once out of the stasis field the trap is sprung. In such a situation, it wouldn't do to let the protagonist see what is in the field, so in stories like this, the story line will not allow normal beings to see something protected by a stasis field. The primary use of stasis fields is essentially the same as suspended animation: to let passengers and cargoes (normally of spacecraft) avoid having to experience extremely long periods of time by "skipping over" large sections of it. They may also be used (such as in The Night's Dawn Trilogy) as protection against the effects of extreme acceleration.

EDIT: In the movie it is referred to as "Delta-Sleep".