Perfectly fine, i did hold off in my first trimester just to be safe but i've had my hair done a couple of times. It's perfectly safe but i'd stick with what 'Miss K' said and steer clear of bleach. Also beware that hair colour sometimes doesnt take so well to preg womans hair (can be slightly dif colour to what you wanted) just be sure to let the hairdresser know and if it doesnt turn out they can fix it. lol

Good luck