You can apply for a Hamad Medical card for all medical expenses at the state hospital once you have your RP's. Their care is very good especially with emergency situations and it will be free.
Also there are some nice medical and dental centres that offer a card for say QR350 to QR400 which allows unlimited dental and medical consultations for a year, you will just have to pay for the procedures and medications. Try and get an extra insurance cover for big emergencies/operations if you can.