I read lots of Zutara arranged marriage fics. All of them were about them getting married AND Katara going to the Fire Nation.
I have nothing against the trope, but it gets boring. So, I have one idea.
In the ancient times, some of the Mongols (I don't know if other people also did it) used to get betrothed at very young age, especially if they were from high ranking families.
The boy's side chooses the girl and they leave the boy at his soon to be father-in-law's home to let them work for them.
Though it is an arranged marriage, the kids would grow up knowing each other.
So, Iroh brings Zuko to Southern Water Tribe (because in the ancient times we never got married in the Tribe. That would lead to incest) and they propose.
Hakoda agrees and Zuko stays at Southern Water Tribe with Katara until they reach marriage age. 👀