Aargh. I immediately dismissed this as silly, but now I can't stop thinking about it.
I would assume this is around Season 3, when the Gaang was infiltrating the Fire Nation? The country is all peeped for a final end to the hundred year war.
For a start, the Fire Nation, unlike Japan, is an expansionist, aggressive kingdom. Whatever social chaos is involved in the transition, they will see the much larger world around them as something to conquer.
The Fire Nation also has technology arguably in advance of 1853 USA, with tanks and airships.
Also firebending. Ships are still wooden then...
Our world has guns and artillery though, and casualties among the Fire Nation will be huge until they adapt.