I don't think there is a specific age on which Quarians depart. They begin training for it very early, and depart when their parents and captain deem them to be 'ready.' That could be as young as 15 or 16, or as old as 20. I'd say most depart the fleet around 17-19 range though.

Remember it can (and often does) take several years for them to complete their pilgrimage.