David
Wattage of hairdryer (on the side or on the packaging?) divided by 12 volts gives the amps required.
Expect the hairdryer to be around 120 Watts (note that a 240V hairdryer will be more like 1500-1800 watts!!). Therefore 120/12 = 10 Amps.
I have one and have connected to my SLA 12 volt battery (Jaycar's 18 Ahr I think it is) and it chews the amps out of it! I'm a bit worried the discharge rate won't do the battery any good.
And if you have a 240V hairdryer around for comparison, you'll quickly see the huge difference in heating between the two. But, any heating is better than none!
Eric