FYI they do not control your passport or bank account.
I've lived and worked in Qatar for long periods of time before.
You -do- require an exit permit, which can be applied for a couple of days before you want to leave the country. That's only if you're working there under a business visa.
Most expats are on tourist visas, which they get extended twice then do a round-trip to Dubai and get a fresh visa on arrival.