My husband has been to the emergency dept. at Hamad several times for non-emergency situations afterhours. It hasn't taken as long as you might think, he's received good care and it's unbelievably cheap. I think if you take your passport and the receipt showing you have applied for you medical card, they will see you at your primary place or just your passport at Hamad. I have no idea where the one is by SR but they usually have a green octagon sign above them. As for appts., the one by me near the zoo is show up and shove your way to the window to get a number. If you want a more pleasant experience and don't mind paying 200 QR a visit just go to Al Ahli Hospital. It's very nice. I take my kids/had a baby there and I'm sure they have a general practitioner.