As I understand it, the cupola was an addition often found along rivers in the United States in the early to mid 1800s, for the purpose of observing the river. I grew up on the Mississippi, and there were a number of old houses with such cupolas. I was told that riverboat captains built them for their wives, so that they could see them coming, but I suppose that's just a story.
The house looks kinda Italianate with the flat roof and brackets in the eaves, which would suggest it was built a few decades after that.
But I really don't know much about architectural styles, so that's a guess.