I work in Wakra and I know that people begin to register their child year round but the official opening for registering for places starts in January. Many of the schools have entrance tests so they also have to deal with that area. I work with KG1 and we usually accept most of the children unless they are not able to separate from their parents.
I also believe that the SEC is requiring that schools accept Qatari students throughout the year unless there is no space in the classes. In the KG1 level we have to accept Qatari children who aren't turning 3 until December.
The other problem is that some schools are not educating the children as they should. Some teachers don't have the qualifications or are brand new to teaching so they don't have the background. There are a lot of factors in dealing with schools in Qatar. People have to do their research and plan and apply as early as possible for possible spots.
The government or independent schools do not cater to English speaking students. These schools are not like public schools elsewhere. My understanding is that in many of the independent school there is behavior problems worse then in the international or private schools. I have been told that often the teachers in the primary schools are not certified, they only have their year 12 complete.
It seems like there are more expats coming to Doha to work so the population is growing.