Hugh Jackman -- New Guard Dog Sleeping on the Job

Hugh Jackman brought a little extra protection with him to the gym today ... and we do mean little ... in the form of his adorable French bulldog, Peaches.

Jackman told photogs yesterday he was still a little shaken up from the incident Saturday ... when an unstable fan broke into his gym, screaming and crying, and threw an electric razor filled with her pubic hair at him.

Clearly he's hoping that if she tries it again ... Peaches will wake up in time to stop her.