Hunting attire or traveling clothes are both correct for what we call a lady's riding habit... my concern is the long gun. For her to walk around port/town with such a garment is fine for traveling... I am just questioning the long gun. Why would she be hunting in town? Why would she be carrying it in town? Hunting, especially for a lady dressed in such a fashion, was pretty much a sport for the well to do...if she is going into town I think odds are she would bring along a servant for protection, and he might be armed. She could be armed as well, but with such an obvious weapon? As for hunting, once she was done hunting odds are she would pass that gun off to someone else to carry as well.
Remember hunting then is done for survival or for sport...those that need it to survive aren't wearing fancy silk gowns to hunt in...and odds are the men of the family are seeing to that task. For sport we are talking about them with the means to do so...not like in the US now a days.