The township includes the villages of Fousetown and Airydale.

Brady Township was named for Hugh Brady, a brigadier general in the United States Army who was born in Huntingdon, Pennsylvania.

As of the census[4] of 2000, there were 1,035 people, 376 households, and 291 families residing in the township.

There were 376 households, out of which 35.4% had children under the age of 18 living with them, 69.4% were married couples living together, 4.0% had a female householder with no husband present, and 22.6% were non-families.

20.5% of all households were made up of individuals, and 12.5% had someone living alone who was 65 years of age or older.