Find your tribe in a Sea of Creativity
irl, colonizers and other dominant groups made dolls of minorities to assert their hegemony and subjugate them, often using stereotypes e.g. https://www.ferris.edu/HTMLS/news/jimcrow/links/essays/toys.htm
These toys were also used to indoctrinate children into particular cultural values or racist ideas. This might be the purpose of Azula's doll. It might be made in EK or FN colonies. Either way, it may represent the colonized EK female, symbolizing women the colonizer can own and objectify. It fits the stereotype of the pretty EK girl from Iroh's song. That might be the message of the doll.
If so, this wouldn't make it better that Iroh gave Azula the doll not the knife. But it shows his chauvinist and sexist thinking that he would use the doll to say: FN women, you can be imperialists too! (just not by fighting or being ruler, that's for boys only).
by @theteashopgirl