Curly hair is not unprofessional, but...
It all depends of what outfit are you wearing. I have some very classic dresses that I wear when I have meetings and would not go well with the "casual" look of a head full of curls. Believe me, I've tried them with curly hair and there's something that does not match, don't know if it's my hair (very much shorter and somewhat poofy and uneven when is curly, regardless of what products I use) but some of my outfits look really good with long, straight (or curling ironed) hair.
On the other hand, I'm sure some of you are going to kill me for this, but I can't stand the look of curly hair in a bun. It does not help at all in making me look elegant. Actually, the only time I wear my hair like that is when I'm at the gym or doing house chores!