You can order the census from your local library. I don't know why it would be restricted with the LDS. I have never had any problem ordering census from them.
This is not the 1871 census but it is the 1851.
Burleigh & Drummer, Peterborough County,

HILL,
G A, farmer, b Ireland, 57
Hannah, housekeeper, Ireland, 53
Arundel, Ireland, laborer, 27
Emily, Ireland, 25
Bold, Ireland, 21
Elizabeth, Canada, 19,
Hannah, Canada, 14
Kate, Canada, 13
Hopton [sic], Canada, 6

I cannot find the 1871 census for Drummer transcribed yet online.
I can find stuff on Arundel & Bold on Ancestry.ca but nothing on Hopkins. Cannot find any of them on 1881 census.

Here is a researcher in the Peterborough area. He is very good and very reasonable. I have used him numerous times. He will look up the 1871 census for you.
familysearch@ontariogenealogy.com