I think the Duggers get their income from rental properties, book deals, TV appearance, endorsement, etc
Perhaps that's the case today. But Mr. Dugger has a job, and that was the main, if not only, income for most of that groups existence.
If they had some inheritance or other windfall that allowed them to obtain property to rent out, fine and dandy. I suspect that there's more than meets the eye here.
While home schooling is fine for some, it's also a means of programing the youngsters for some sects; occasionally dangerous ones. And let's not forget the health concerns of such numerous births on any woman.