Yes, Qatar has a zoo. The Doha Zoo is being renovated. It is scheduled to reopen 2017.
Qatar also has a wildlife preserve but it isn't open to the public.
The Al Wabra farm is an oasis of green areas, palm trees and many rare wild animals from allover the world. Powered by Sheikh Saoud Bin Mohammed Bin Ali Al Thani’s passion for nature, an international team of expert vets, biologists and keepers are dedicated to the care and conservation of the rare and mostly endangered animals that can be found on the farm.