If he is taking a cut in salary and your business will be stopped (no income there) - you are better off in the US. Qatar is expensive. Full stop. Better packages include housing or a reasonable housing allowance, tickets for the family every year, medical, reasonable education allowance (private schools are not cheap - even if you are homeschooling, good packages include this) and in most cases a transportation allowance. If the package doesn't make sense economically - don't come. The rest is immaterial if the $$ doesn't make sense.

Expats come here because of the $$, and for no other reason (unless you are in the US military).