Go for HMC Medical card if your company is paying her medical expenses....

Visit Health Centre at Al Dayyen (that is where they'll send you anyways, until you have wasta) along with your Kahramaa bill or tenancy contract, her ID card & Passport copy (just in case) & pictures.. They will give you a form, which you have to submit in Al Khor/ HMC or Wakrah hospital, which ever is closest to you along with 100 Riyals and get your medical card.