References to the CSS PONTCHARTRAIN being on the White River:
ORN 1, 23, 171 (dated June 19, 1862): "There is now but one gunboat remaining in White River, the PONTCHARTRAIN, mounting three or five guns, etc." This statement is confirmed again, on page 197 of the same volume, by CS General Hindman.
However, at a later stage she seems to have moved to a position either at, or near Little Rock, where she was last reported, in August, 1863, as being fitted out. I can find no additional documentation in the ORN, on that vessel, after that date.
If you are able to locate official documentation that she was destroyed at Little Rock, in September, 1863, and not a month later, it might be advisable to inform the compilers of the DANFS, so that corrections can be made in future editions. However, I would assume that they obtained their information from reliable sources, unless these reliable sources themselves were in error.