I think you would be much better off paying for private school for your child and continuing to rent an apartment for at least the next three or four years. The housing crash has just started, and buying anywhere in your area in the next 12 months is likely to be a VERY expensive mistake. I think a 50% drop from the highest prices seen so far is a very conservative estimate; 80% or 90% may be more accurate, given the unwinding of the mortgage insanity as well as the other serious economic issues that are going to clobber most people without their having a clue.
There won’t be any hurry in buying after the bottom is in. No one will want to talk about real estate for a long time, which is when you want to buy it.