I was sorry that I dragged my own hair dryer on the ship last month. I was in cabin 6042 and the hair dryer in the bathroom there was definitely strong enough to dry my hair. It wasn't the absolute best blow dryer but it was much better than I had anticipated. The only problem was that as you were using it, it would heat up pretty high, so I ended up wrapping a towel around it, and then it was fine.
As for bringing your own, you can plug it in over by the desk area, in front of the mirror, but bring a regular household extension cord, with a regular end on it. The outlet does take 3 prongs, but its very low on the desk, so if your blowdryer has one of those large square ends on it, like mine does, it wouldn't fit. With a regular household extension cord (I brought one of those white ones that they sell everywhere), you could plug that into the outlet, then plug your blow dryer into the extension cord. (Hope I am explaining this correctly. lol).
I won't bother dragging my blow dryer again, but my hair is medium, not very thick. If you had very long or thick hair, maybe you'd want your own.