as e4 mention ... ASD or DESS, Park House and Doha College are among the best one. Depend what curriculum you want your kids to follow.

with the housing prices now ... you will need at least around 15.000 QR for 3 bedroom house or more (especially with the size of your family). Can't you push more allowance, except you prepare to fork out more from your salary. Or best if you ask the company a house not an allowance. Safe the headache with the rents hikes every year.

And as e4 said ... school always waiting list. Make sure you sort the school out before uprooting the kids.