I've read that "Fräulein" is offensive to use towards women because it's a diminutive, and that "Frau" is better to use for women, but would "Fräulein" be considered acceptable for young girls, since they're basically young women, or would it be taboo for girls too?
Answers to this can only be largely opinion-based, so this is only my perspective, I think "Fräulein" or, better, "junges Fräulein" is still fine as a half-funny old-fashioned sounding address for a child. However, the term is a bit loaded, and some more feminist parents might not like it. Children might not even know the word.
An easy way to circumvent trouble would be to just use "junge Dame" instead.
What I wouldn't do at all is call a child "Fräulein Mayer" or "Fräulein Laura" or something like that. This kind of address has been dead for decades and won't come back. I would also not use "Fräulein" to address a teenager or anyone older that that.
Just to stress this once again, there is no broad consensus about any of this.
Using "Fräulein" to address a young girl (I'd say up to around 10 years old) does not carry the same generally offensive connotations to me that it would it used for women or older girls. However, it is not common usage. If your interest is for personal use in interpersonal communication, I would recommend against it.
There are two contemporary scenarios I can picture where using "Fräulein" does not feel out of place to me: One is as part of a verbal scolding, similar to how some parents would use the full name of a child (as opposed to a nick name) to indicate that they are serious and annoyed. The other would be by a butler or waitstaff in a highclass restaurant, who emphasize their class by using antiquated language. Here, however, "junge Dame" would work equally well.