Unfortunately, that is the situation on the ground with regards to admissions at almost all schools here. Recently, a news item appeared which stated that the government was contemplating allowing some schools to work is two shifts. You may write to the Supreme Educational Council and seek their help but don't be too hopeful of getting a positive result. You may need to fall in queue and wait as some of the schools have suggested to you and the wait may be that long. Yes, your children will not get admission in any school if you or your wife don't have a Resident Permit. However, getting a RP is an easy process and it can be obtained within a week of arrival in Doha.