There is definitely a demand. I'm not so sure about private tuition though. There are all sorts of regulations regarding work in Qatar. The English Language (TESOL, TOEFL etc.) tuition centres pay pretty well I think. One school I know of pays QR 95 per hour if you are TESOL certified. Working hours are flxible up to about 40 hours per week.

If this is a second income, QR 16k odd per month is not to be sneezed at.