Tom, as far as I know a roster for the Nancy Hart's never existed. It would appear that the full name of the soldier from Company K 2nd Georgia State Guard Cavalry was William Young Mooty. It also appears that he married Mary Ella McKemie in 1860 and the couple had 11 children the last being born in 1888 and the first being born in 1862 and that Private William Y. Mooty died about 1912.
I rather doubt that she played a military role after looking at George's information concerning the CMSR's for William Y. Mooty ie enlisted in August of 1863 and was absent due to sickness in January of 1864. It would appear the couple had their second child in 1864. For some men the opportunity to comply with Confederate conscription act and only serving for six months, which seems to have been the case with the 2nd Georgia State Guard's Cavalry may have been a godsend. Governor Brown of Georgia resisted the Confederate military draft and helped to keep many of its military male citizens within the State of Georgia and an example of this would be the 2nd Georgia State Guard's Cavalry. Governor Brown was not always successful in keeping his State troops and militia in Georgia however.
Why Mary has an iron cross on her tombstone at the Mooty Cemetery is unclear. I can only try and lead you to some roads to explore. Mary does have a death certificate and may have an obitz in February of 1923 in a local newspaper or perhaps the newspaper in Columbus, Georgia. It would appear that Mary may have many living descendants great grandchildren since she had 11 children. In many families someone has an interest in genealogy or family history and try to find out who that person is and what stories they might have to pass on. Mary may have been affiliated with the United Daughters of the Confederacy.
If it is a government Confederate tombstone then it was likely made by the Blue Ridge Marble Company out of Nelson, Georgia. They had the contract in 1908 for all Confederate tombstones but I don't know how long the contract was for. I would not be surprised to learn that her children had the tombstone privately made for her including the iron cross to symbolize her commitment to her husband and or the cause. I don't believe any legal laws would have been violated. Please keep us updated as to your future finds.