Teenagers could entertain themselves with various activities.

If they like water sports they can join clubs in Doha or participate with groups (like classmates or community group) and arrange functions like camping by the sea shore (enjoy desert and sea at the same time). The places are safe here to stay overnight camping. Also there are diving clubs and sailing clubs. Fishing trips are available.

So, to conclude, if they like nature then they will have fun. But nature here during Summer is tough.