Was the jar made during the 19th century?
This type of jars were also made in the Guangxu reign (aka Kangxi revival), often with double ring marks.
The peonies look indeed like Kangxi style, so does the shape. Is the neck glazed or not? I feel that this is Guangxu despite the resemblance, because these were probably more common then, but I would still advise to look out for jar of the exact same type that is confirmed as Kangxi. I have the impression that the type of blue and whiteness of the white glaze is rather later than Kangxi.