I just arrived in doha 11 days ago...
(Thanks for all QL members who always respond to new comers questions like me and also give support not to give up). I want to share my " School Search" so you get an idea.

I send the application to 3 schools on July (2 months ago).
And just get the waiting lists. Since my kids only 6 & 5 years old, it's a long list... . For older group the list is shorter :).

Then when I arrived, I called all the schools tell them that I'm in Doha with my 2 kids. They will give priority if the kids is already here. Then I made appointment to visit the schools and meet the admission staff. I got appointment, and bring the kids there just to tell them "We're here and we're serious to choose the school" (also because I don't have much option :) ).

Then, my husband and I take turn to call the admission staff to arrange the assesment for the kids, every day.

After a week, we got an assesment test for the older kid.
And, thanks God, he can join with the school.
The next day, when the older one go to school, I bring his younger sister to school and meet the admission staff to say thank you, that one of my kids can join the school, hopefully his sister can join the school.

After 2 days the young one take the assesment test. Next day join the school. Happy ending. Today is the 2nd days they're in the school. So far they are happy.

I hope this can give you a clue a little bit.
Some school also give priority to some company's employer.

Kind regards.