You will need to pay for your children's education because I am sure you would not be satisfied with the public schools here and your children should be fluent in Arabic besides (but maybe they are). However, if you get a good job they usually provide an expat with the cost of educating their kids (at least up to 2-3 kids).

I would suggest renting for now as I don't think the Pearl or Zig Zag towers are good for living with children (no yards or parks). However, supposedly Lusail will have housing tracts that have individual villas at some point. I do think buying in Qatar is way overpriced at this point and not a secure investment for a non-citizen. You can rent a 3 BR villa starting from about 10,000 QR/month at present, and most companies will pay for housing.

Have you tried Vodafone?