I can't really understand what "becoming of her" means here, but to me it sounds closer to she was acting appropriately, or correctly. This is not what you intend.
It was very her could possibly work in a very colloquial way, non-standard way. Similarly, that was very her of her is also possible. But I think the more common way is with so. I wasn't sure of the best definition for this usage, but this one seems to fit:
not standard used before a noun or before "not" to emphasize what is being said:
Don't wear that - it's so last year (= it was fashionable last year but not now).
I'm sorry, but she is so not a size 10 (= she is very much larger than a size 10).
It's colloquial. It's way to emphasize that the action is a characteristic or style of the person in your case.
She suggested we go to an underground rock bar. That's so her.
That's so like her.