Endocrinologists are highly specialist, so I would be very surprised if you had a massive choice. In small places like Qatar you would normally have really maybe two of them! They are most likely to be employed as consultants (working for a few hospitals), so it really isn't like picking a good dentist. In reality, if you go to check out all the hospitals you may discover that they all use one Endocrinologist.... and that guy/lady would also have private practice. So... don't go crazy on going private if you don't have to, as you're just likely to pay crazy money for the service you can get for free.
Endocrinologists are highly specialist, so I would be very surprised if you had a massive choice. In small places like Qatar you would normally have really maybe two of them! They are most likely to be employed as consultants (working for a few hospitals), so it really isn't like picking a good dentist. In reality, if you go to check out all the hospitals you may discover that they all use one Endocrinologist.... and that guy/lady would also have private practice. So... don't go crazy on going private if you don't have to, as you're just likely to pay crazy money for the service you can get for free.