Im not 100% sure about the EAD. But i thought she had that on her POE. It says work authorized on her SS card. And yes hopefully her card will be approved with no interview.
You should have still filed for her EAD(form I-765) as part of her AOS packet (I-485). K1 visa holders are not allowed to work until they receive either their EAD or their permanent resident card. Her SS card should say "work authorized only with DHS authorization."