Hey Arjal,
Ive been in Qatar for a couple of years. I can confirm that if you receive an offer (Make sure its a Family Visa) that you would not have any issues with a step child. This is offcourse only if you have the correct paperwork in place for everything. They are very strict on all paperwork.
You would need something along the lines of:
Unabridged birth certificates (Wife and stepchild)
Attested Marriage Certificate
All Qualifications Attested and translated to Arabic (Yours)
Also for QA obviously current Medical and all that jazz.
They should provide housing, and funding for school. Just be careful, as there are a lot of schools that have a HUGE waiting list.
Also, depending on what equipment you are rated on, the requirements have recently changed.
Hope this helps you a bit.
Maybe consider looking at a wider variety.