Hi Dominic. If you r planning to bring them on a tourist visa, wouldn't you be able to take a travel/tourist insurance? the likes of which cover, flight delays, mishandled baggage, emergency medical care while travelling. I believe the premium is calculated based on age of traveler and duration of stay abroad. it probably wont work out to much. it will be either cashless treatment or you pay upfront and then apply for a reimbursement. Of course, here's to hoping that your family will have a happy and illness free time in Doha

As for clinics, why don you try the Aster clinics. They have quite a few branches in Qatar