You haven't made a mistake at all! The little girl will love it and love you for buying it!
The Barbie phenomenon is massive-- too big for me to take on single handedly (prefer to save my battles for more important things) which is I let my girls have them, but I do maintain a heavy-handed cynicism about Barbie in front of them. When they play with their Barbies I'll put on a girly squeaky voice and say 'Ooh, no chocolate biscuit for me, thank you, I had half a lettuce leaf last month and I'm still full up' and things like that. (Also like to pretend that one particular pink and princessy Barbie (Rapunzel?) in their collection suffers from bad wind.) At the moment they think its funny but one day they will understand why I dislike her so much!
My argument is with Mattel. Just wish they'd update her to being a more realistic shape, and move her away from her grubby roots under the newsagents counter.