The goblin's haunt or beat. Dobby is an archaic word for a goblin or brownie. (See Washington Irving's Bracebridge Hall, ii. 183-6.) Dobby also means an imbecile old man.
“The Dobby's walk was within the inhabited domains of the Hall.” —Sir W Scott: Peveril of the Peak, chap.x.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Dobby's Walk from Infoplease: