my in laws visited last year and left in December. I was the sponsor and went to the ministry of interior office in Wakra and paid QAR10 each to get an exit permit for both about 3/4 days before they exited the country. if an exit permit is not required then i would expect them to have told me this when i went there but they charged me QAR20 in total for the two exit permits (so no gender discrimination here). the in laws however did stay for just under 3 months. currently my mom is visiting me and i am not taking any chances and am planning to go to the same office and pay the QAR10 to get an exit visa for her a few days before she leaves.