Good Luck on school admissions. Its next to impossible to get a school admission without an RP these days. The Govt. is very strict on admitting kids on family visit. Schools are also facing problems when kids suddenly disappear when the visit visa expires.
Moreover most of the schools have closed admissions early this year since the Ministry has restricted the number of students admitted per school.
Better get the RP and then try for admission or else you might not stand a chance. Honestly you wont even get an application form if you don't show the RP.
Why did you come here on the first place without family RP? Visit visa don't do any good anymore here in Doha.