I believe you indicated Dorothy Arnold Crotwell died about 1818.If so I doubt there will be a death certificate as these were usually not required untill sometime after 1900 + by many states.Need to check with the suspect state & county for that.
I don't have info on the Arnold family.If born abt. 1888, Dorothy Arnold should appear in the 1900 census as abt. age 2 plus or minus with some family, and in the 1910 census about 12 years old plus or minus. If she was adopted or raised by Charles & Rhoda Arnold Davis she may have been listed with them.
I am not descended from your Robert Crotwell.I am in GA.