While working in Asia - Indonesia and China - I picked up some pieces of purported Ming and Qing dates but one vase is of a quite different type - thin necked and with a small hat but wide at the base. I got it from Roti, the last most southern island in Indonesia and I wonder if it is genuine.
This is probably a water flask with lid, Its style is "Persian" or "Islamic". It is probably from the Dehua Kilns is Fujian.
Blue and white porcelain was made there too but not much, since the color of the blue turned out in the watery style your flask got which was not as popular as the porcelain from Jingdezhen.
I am not entirely sure but that is what - form my point if view - looks most likely.
I would by no means call it a "fake" - it is probably most seriously made for a purpose, I would have guessed for some kind of export order, but a date is hard to put on it anyway since the shape is unusual.
A best guess would be mid 19th century since that would match with similar pieces decorated in Rose Medallion and intended for the North American market.