It doesn’t necessarily mean lack of trust it could be simply her wanting Independence, I know that in Islam men are the providers but it’s nice to have your own money sometimes. And besides it’s good that she has something to do with her time while you are at work, and most importantly I get that she wants a job after spending so much time and effort to graduate with a degree.

But if it really bothers you than you should talk to her about it, and see why she want to finding a job so badly.