I just learned all about this. If you're working and she is under your RP then it should not be a problem, I am assuming she has RP as well, you just need to apply for a health card at the nearest Primary health center. If you have the Marhaba book the list of facilities in each area is provided.
Make sure you take with you her passport, resident permit, one passport photo and 100 riyals. The health card is issued same day (at least in my case).