Jennifer, I have been researching the Murdock family in Horry/Georgetown Co. According to the will of James Woodward, Sr., his daughter, Tabitha Ann, married a Murdock. The only Murdock I find in the 1800 and 1810 census is James Murdock. He apparently died before the 1820 census and Tabitha Ann is listed as widowed. I suspect James was in the war of 1812 and possible died there. She died before the 1850 census. They had two sons, John and Joseph. I suspect their son, Joseph, is your Joseph Murdock. Let me know if you think this may be a match.