A technique for replicating a data object from a source data storage system (source) to a destination data storage system (destination) preserves QoS (Quality of Service) by transmitting QoS information from the source to the destination and applying the QoS information when storing data at the destination that arrive in replication instructions sent from the source. The QoS information indicates desired storage tiering for the data object at the source. In the event of a failure at the source, which results in failover from the source to the destination, the destination is able to provide users with the same quality of service as was desired at the source.