I can understand your desire for the gift to be a surprise, and only you know whether your daughter would prefer it that way. There might be some advantage to her being part of the selection process, however. My daughter LOVED looking through the options displayed on the website and deciding which one she wanted. The website allows you to get a doll which combines different features (skin color, eye color, hair color, hair curliness, etc) if you want one looking more like her, by the way; that's what we did. I did end up suggesting we get the one with hair and skin more like hers, but that's because she is biracial and I felt it was important for her to have a doll which celebrated that 'look' instead of accidentally supporting the idea that beauty is only light skin and long straight blond hair. Based on your post, those considerations aren't important for your situation; I'm just mentioning why it was important for me that our daughter was involved in picking the doll.
Anyway, she was thrilled when she got to open the package at her birthday party even though she knew what was in it, and she has loved the doll. I will also add that additional outfits often are not tied to a particular doll, so don't let that determine what you get.
Have fun with it!