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).
Peverley, who was not drafted, made his professional debut during the 2004–05 season with the South Carolina Stingrays in the ECHL and then played one game in the American Hockey League (AHL) with the Portland Pirates.