Undrafted, Peverley made his professional debut in the 2004–05 season in the ECHL with the South Carolina Stingrays before playing a solitary game with the Portland Pirates in the American Hockey League (AHL).
Undrafted, Peverley began his professional career in the 2004–05 season by playing for the South Carolina Stingrays in the ECHL before making a solitary appearance in the American Hockey League (AHL) with the Portland Pirates.