Dovre Township was organized in 1869, and derives its name from the Dovrefjell mountain range in Norway.

As of the census[1] of 2000, there were 1,968 people, 708 households, and 589 families residing in the township.

There were 736 housing units at an average density of 27.1 per square mile (10.5/km2).

There were 708 households, out of which 38.3% had children under the age of 18 living with them, 79.1% were married couples living together, 2.5% had a female householder with no husband present, and 16.8% were non-families.

13.3% of all households were made up of individuals, and 4.4% had someone living alone who was 65 years of age or older.