For 1st bday in a Hotel in Doha, that means the child only starting to walk and the guests are parents and toddlers---for a large group towards the end of summer, try the outdoor poolside of Intercon at Dafna where there's a baby pool and ample space for eating and running, and little distance from the adult pool.  For small to medium group, try Animato restaurant in Movenpick apartment and suites at West Bay.  Food is great and there's a play & food corner for toddlers.  You may seal off the area when booked. Enjoy your time!