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For rods and fishing accessories, try Jassim Al-Lingawi Trading. There's another smaller place about 3 doors down and another marine supply place across the street. Search for these coordinates on Google Maps: 25.288121,51.539391.
I haven't been able to find good one piece rods. Happy Fishing.
Go to Carrefour in Doha City Center, look for it at the back of all those garden seating setup display or ask someone when you are in there.