I know of nothing that should prevent her from becoming a vampire.
Traits.remove_trait SpecialNPCs_BabyAriel should make Ariel mortal again, but then the game will create a (differently looking) replacement with the same trait.
You could also try baking a birthday cake, inviting her and aging her that way. (I haven't tried either method myself, because I play with aging off and my mortal teens, too, will stay teens for a long time, so that Ariel being technically unaging makes no difference.)
And I'm weirdly glad that they put in a celeb that I had no chance of knowing beforehand or ever seeing due to my interests (and probably age). Because of that she's just another premade to me.