Yes he come anytime to Qatar and all you have to do is apply for a visit visa at Ministry of Interior in either the Immigration Office in Gharafa or at the building near to the airport.
Or to ensure that everything will be okay just contact any travelling agency here like the Cleopatra Travel Agency in Musherib Doha and they handle everything and they will brief you for the necessary requirement needed by your father before he come here.
Hope that this will help you.