Al Gharafa is fine - for the most part no section of Doha is that much better or worse than any other. Unlike some other cities in the world, the expats are not concentrated in particular areas - so anywhere you land will be fine.

As for schools, Compass is right there in Al Gharafa and is the school that my 5yo son attends. Sherbourne isn't too bad of a run from Al Gharafa (I don't think it is, anyway).

Like ominstructor said, getting into a school is going to be your biggest challenge.

Good luck!