I've had friends and cousins' kids go to the Bear Creek School with very good results! It's great that you're starting over a year in advance because some private schools require interviews, etc. The Bear Creek school also has pre-K programs as well, but you can only get in if there's space, and only if your child is "ready".
Openings fill for September starting in the spring (like March or April before the school year in September). Even at the public LWSD schools you need to register in March or so - especially if you want an all-day kindergarten (ADK) program (which if you want strong academics you'll likely want).
Be aware that LWSD charges extra for ADK, and they are only required by law to provide free half-day K. Some schools have a lottery program or first-come-first-served all-day-K program, and not all elementary schools in LWSD offer ADK even then. To figure out which LWSD school your child is "supposed" to attend based on where you live, go to http://www.lwsd.org/Schools/School-and-Bus-Finder/Pages/d... Once you know that, you can go there to either register your child, or get a variance (permission to attend a different public school within the district). Make sure you have your child's birth certificate and/or passport and full immunization records the day you go to the school to register.
If your neighbors have kids - even older ones - MAKE an opportunity to ask them where their kids go/went to elementary school. It's always good if your child has someone in the immediate neighborhood going to the same school as you and other moms might be able to carpool, take turns waiting at the bus stop, or they might know things pro/con about specific schools/programs/teachers.