It's very difficult for children here in the summer.
Other than ice-skating I can't think of much in the indoor activity area.

We usually keep our kids busy for the part of the summer during which they're in Doha with beach/swimming, board games, structured computer/Playstation time, art, music, cooking, water-gun fights and with the guidance of the eldest home-made plays.

Expect to hear "I'm bored" frequently.