How can I change the controls in Don't Starve?
Probably wasn't available when question was asked:
From Main Menu, go to Options, Pick Controls, and you can set custom keys.
Don't Starve is mostly controlled by mouse. You are only able to walk around using the WASD keys.
Please see below, for reference.
http://dont-starve-game.wikia.com/wiki/Controls
Alternatively, you could use AutoHotKey.