Ok so while I have posted our experience I just thought it may be useful to post a little more information in case anyone tries to do a Google search or something the same as I did… maybe it will come up, maybe it wont.
Qatar Exit Permit – All those with a Residents Visa need an Exit Permit to leave Qatar, which must be approved by your sponsor. If you are under a Work Visa your employer has a process in place, which includes handing over an internal application for an exit permit along with your passport a few days prior to leaving the country. Apparently most require a confirmed booking to do this. They then take care of the rest and return your passport to you prior to your departure date. If you are under a Family Visa you only need an Exit Permit if you are a Husband (or I think male child over 16, but not 100% sure about this one). The easiest way to do it is either online (but the online form on the MOI Website is only in Arabic), or to just go out to the immigration office next to the airport (first left and then left again after the airport heading into town along Old Airport Rd) with your sponsor who can sign the form on the spot. The actual forms at the immigration office are in both English and Arabic, so hopefully the one online will be the same in the near future!
The reason for the Exit Permit is (from what I understand) so that those who are under residency visas do not just leave the country leaving money owing, breaking employment contracts etc. I am guessing the reason why husbands (but not other dependents) under family sponsorship need one is for similar reasons, and possibly that if the male of the household leaves the country there is more chance the wife may follow.
Of course there is one problem with all this… there is nothing that I can see that would stop you from getting a return ticket and Exit Permit to fly to somewhere nearby, then booking a flight home from there… but maybe I am wrong.