From the tombstone, we know her name was Arabellar Murphy, wife of R. Murphy, and she was born 18 October 1826. The stone is broken so we can not see her death date. A tombstone beside that of Arabellar marks the grave of David Murphy, son of R. & A., who was born 14 November 1854. There is no death date.
The Murphy family is found only on the 1850 Livingston County census. Richard Murphy was age 25, born in Virginia and was a flatboat pilot. Arreller [sic] Murphy was 24, born Tennessee; William Murphy was age 1, born Tennessee and Joseph was age 4/12 born Kentucky.
Much more was found in Kentucky Vital Statistics (Deaths). It appears Arabella Murphy was born in Montgomery County, Tennessee and was the daughter of Sarah and Jackson Allbright. Arabella's death date was listed as 27 November 1854, age 30. Also listed was David P. Murphy, age 3 months when he died 28 February 1855. If David was 3 months old when he died in February, he was born right before his mother died so perhaps Arabella died from complications of childbirth.
A search on Ancestry.com showed two marriage records of interest. Richard Murphy and Arabella Albright are shown marrying 30 October 1849 in Dickson County, Tennessee and also 13 November 1849 Stewart County, Tennessee. It is possible the earlier date was for the marriage bond and the latter date was the actual marriage date. Kentucky allowed marriage bonds and licenses to be used in any county within the state. To be sure, though, that these are the same people, copies of both records should be examined.
I have not found where Richard Murphy went when he left Smithland. As a flatboat pilot, the possibilities are many - perhaps Nashville; Cairo, Illinois; Evansville - but somewhere on a naviagable river most likely.