I think that anything permanent should wait until she's old enough to understand all the implications of her decisions. Girls' brains aren't fully mature until age 23 or so! (Boys' brains mature around age 25, some even later :)
So if you feel up to being a good parent that will consistently enforce rules, tell her that she can do anything she wants after age 18 (legally) but hopefully up to age 23! I know you're not thinking of this yet, but how will you handle requests in the future about other "permanent" issues, such as piercings, tattoos, getting married, getting pregnant, name changes, etc.?
Tell your daughter to name her dolls whatever she wants. When she's older, let her go crazy with temporary tattoos, hair color, weird clothes, etc. But the permanent stuff really should wait.
I'm sure there are a lot of folks out there who regret some of the stuff that their parents let them get away with too early.