First, you as Asylee (the same applies to your wife) don't need EAD in order to get a job. All you need is unrestricted SSN - she can apply for one in ten days after arrival, and government issued ID. By law employer can't tell you WHICH documents they will accept as proof of your eligibility to work. But if she wants to get one (I did applied for one so it's less hassle explaining all the time what is asylee and how ''to eat us") she has to file I-765 - application for EAD.
