" you have nothing to worry about"
Well...be careful..just make sure you don't any mortgage in local bank here.
Indeed they won't let you out (not Qatar airways but the local authority)in case you resign or got terminated and have some big debt left behind...interesting scenario...: no Job, no revenue and stuck in Doha with debt..it happens before.So just make sure you pay all your "bills""and fines..and think twice before applying for a mortgage from any local bank.
I don't think qatar airways can prevent you from leaving the company,although I knew a few case where the company refused the resignation of the pilot in first instance..but I don't think its in their interest to keep a pilot who doesn't want to work for the company.
And honestly and after so many years I still haven't got the meaning of this exit (or multi exit) permit. At the end of the day they can always block you at the airport,if they have to,even if you have an exit permit or multi exit permit.