So you know your moving your family of four in six months to an inflated market. We all know the bubble will burst, question is when? Do you rent and move again when the time is right? Do you build new? Do you buy and ride out the market but keep your family stable and settled? The not moving again is a biggie for us this will be move number 17 and as a civilian finally the stability option carries some weight.
I was going to say, I'd rent, but 17 moves...wow, that is a LOT! Different consideration for you.
Personally, when moving to a new area I would always plan to rent. Granted, I have a small family and not a big 2500 sqft house of possessions to deal with, but I definitely prefer to be boots on the ground for at least 6-12 months in an area before I want to tie myself down to a specific neighborhood or area. I'd hate to rush to buy something in a part of town I really didn't have a feel for, even with the advice of a good agent or locals. Not even just in terms of crime, schools, etc but also in terms of lifestyle.
How do you know the market is inflated? Is it overvalued now or was it undervalued then? We all know the bubble will burst ... do we? How do you know it is a bubble? What market are you referring to? If it is a strong market, you find a great deal relative to current fair market value, can force some appreciation, can afford it, and are willing and able to hold for the long term, then why would you care? If it is not these things then it is probably not a good idea to buy, ever, or at least until these things are true.