I find Harriet Beasley as you stated on the 1880 census age 33.
The 1870 census has her in Manteo living with Mary Beasley age 47. Probably her mother. there are also Polly age 26 and Willian age 14. Harriet is 23 at this time. (The transcription is given as Brasley)
The 1850 Roanoke Island census page 8 has Mary age 27, Frances age 10, Ada age 5, Harriet age 3 and Nancy at 8 months. There is also Ada age 69. The last name is transcribed as Lindley but I am more inclined to read it as Quidley.
The 1860 Roanoke Island census confirms the name to be Harriet Quidley age 40. Mary is age 37, Adda age 14, Harriet age 11, and Nancy age 8
The imformation on the census records indicates to me that the maiden name for Mary, age 37 on the 1860 census would be Quidley ahd that Harriet may well be her sister.
1850 census page 10 There is also a Thomas Quidley age given as 1 living in the home of Nancy Brickhouse (Roanoke Island) He could well be another sibling of Harriet. The Basterdly Bonds for Currituck may be good source of imformation in order to expand the search.
I find a Harriet Quidley age 30 on page 1 of the Roanoke Island, Currituck Census Record.
At this point, I would venture a guess that Harriet Quidley age 30 on the 1850 census is the mother of Thomas
I found no adult men in any of these homes.