The FreeCen transcription project is ongoing. Their database coverage gives some idea of how complete the coverage is for each county in each census year.
In the case of Dorset, we see:
1861 - 46,737 individuals, representing 26.7% of the population listed in the the census.
1871 - 30,050 individuals, representing 14.1% of the population listed in the the census.
(figures updated on August 12th, 2019 12:16)
Try asking at your local library or archives to see if they offer access to Ancestry for local residents. Many now carry the Ancestry library subscription, and sometime access to other genealogical databases.