Personally I would not run a 12V hairdryer from the normal 12V sockets as the cable feed and connections to these is only thin gauge and could overheat or even catch fire, you will also run your battery down very quickly if you have not already blown the fuse.
If you look at the sockets in your car you will normally find that only the one with the cigar lighter will be fed by thick gauge cable and the socket itself is different.
Why not do it in the car with the engine running?
If you really have to do it I would wire a socket directly to the fuseboard using suitable size cable and fuse.
We have 3 way car type sockets wired direct to the fuseboard but the heaviest current devices we use are a beer cooler(and then only on hookup) and an LCD TV, we also plug in phone chargers, games, satellite and DVD players when required.
My wife and 2 daughters all have very long hair (close to waist length) and we let their hair dry naturally or by towel and hand method - even at home most of the time.
