I don't know if this will help you, but my Louisiana Murrays are in the Livingston, St. Helena, and Tangipahoa Parish area. There were three orphaned children in the 1850 census living in the household of William Wells and Lavinia Durbin. One of the children was Mildred Murray, age 9 [est'd birth about 1841]. Mildred was still living with William Wells in the 1860 census [mostly illegible unfortunately]. After that I never found any more information on her.
I was told by another researcher years ago that these orphans were children of the late Elihu T. Murray and Delilah [Richardson?] Murray. William Wells was appointed as their "tutor" in the 1840s - this implies there's a court record somewhere with potentially more information. Also note her mother's name Delilah, an intriguing coincidence.
I was unable to find any information on Elihu and Delilah at the time this research was done [in the 1990s], so I don't know if Elihu is related to my Murray line, but it seems likely. I haven't tried to research him in recent years, now that there are so many more records online. Maybe you'll have better luck.
I did find a 1916 confederate pension record for your Mildred, which mentions she married C. R. Cooper on 14 Apr 1869 in Pearl River. [Browse several pages to see the whole file.]
I hope this helps lead you to more clues!