Dave, A close-up partial picture will usually provide the best pictures for checking age signs, color tone of blue and white ground. Usually, the most important places are the foot rim, foot (whole or partial) top rim (inside of the neck), and any places with dark spots or glaze constructions. Next time you could upload pictures somewhere on the net, like Flickr or similar, and then post the link. These jars are quite large and the size limit can make it difficult to upload images with sufficient resolution.
Anyway, in this picture I think we can be sure the jar is old. The base circumference sure looks old.
I can't help with the carving though, I have no knowledge whatsover regarding stone carvings. :-)