The Red Hat is a type of headgear exclusive to Nintendogs that is based on Nintendo's main mascot, Mario. It is a counterpart to the green hat, which is based on Mario's brother Luigi. It can be obtained on walks. It sells for $20.
The hat is dome-shaped and red all over, except for the front where there is a white circle with a red "M" in the middle.
DS: "This hat is standard gear for mustachioed master plumbers."