" only carried a cane and a billycock hat to make her boyish"
Example of a cane and billycock hat
Public DomainExample of a cane and billycock hat - Credit: Albert Edwin Roberts (1878-1964)
The actress, Olga Petrova, wearing a billycock as a riding hat (1915)
Public DomainThe actress, Olga Petrova, wearing a billycock as a riding hat (1915) - Credit: unknown

A cane is an old-fashioned word for a walking stick.

A billycock hat is any round, low-crowned, felt hat, an example of which would be the hat commonly known as a bowler.