A hair dryer is actually a quite heavy load, one of the highest that an inverter will see. My wife's hair dryer is rated at 1500 watts on high. So you'd need to be looking at a 1500 to 2000 watt inverter, pure sine is best, and around 300 AH of batteries. I'd personally let my hair air-dry, but I am about bald, it takes about 3 minutes...
๐ The main issue with batteries is actually less the amount of energy you will pull out of the batteries, which will be 125 - 145 amps at 12 volts nominal, since you will probably only use the hair dryer for 5 - 10 minutes a day, but the quite high rate at which you will drain the batteries for that 10 minutes. That needs good batteries and quite heavy wiring. This won't be a plug into the cigar lighter kind of deal, it will be custom made cables that are about a half inch in diameter.
Once you get into that kind of inverter you need to deal with the battery charging, you may already have a good modern 3 stage charger in your converter which would do fine, but if you have the old style Magnatech converter still installed you'll want to either look at inverters with a built in charger or a converter upgrade. You'll want around 45 - 55 amps of charger to charge the batteries you'll need reasonably quickly.
Hope this helps
Brian
2005 F250 Supercab, Powerstroke, 5 speed automatic, 3.73 gears.
20 ft race car hauler, Lola T440 Formula Ford, NTM MK4 Sports Racer
1980 MCI MC-5C highway coach conversion
2004 Travelhawk 8' Truck Camper
