New Bellmere State School is fully functional. They are a BYOT (bring your own tech, currently Apple based) school. Most State Schools in the area are strict on catchment zones, so be sure your new address falls within the school zone of preference. This ensures one school is over-populated than other schools build to reduce loads on others. I have also taken the liberty of notifying realestate.com.au of the omission of this new school on their website. It should be fixed now, and will show up in property searches.
Bellmere doesn't have a primary School itself. However you will find that School buses run out of Bellmere daily to Caboolture where you will find St Paul's Lutheran Primary School 55 Smiths Rd Caboolture, QLD, 4510