Assuming that the connector is configured correctly, you should already have a custom field in Rally and a custom filed in QC, which you have created for the purposes of this integration. Both are referenced in the connector's config file as ExternalIDField under respective sections.
When a defect is successfully copied from QC to Rally,the connectors writes
a) the ObjectID of the newly created Rally defect to the ExternalIDField in QC.
b) the ID of the original QC defect to the ExternalIDField in Rally.
The connector keeps track of associated artifacts between the two systems via these custom fields.
If upon the creation of a new defect in Rally the original QC defect is not updated with the value of the Rally defect's ObjectID, the subsequent connector run will result in duplication of the defect in Rally because QC defects with empty ExternalIDField are subject to copy service. QC defects with a non-empty ExternalIDField are not subject to Copy service - they are subject to Update service.
Make sure that the defect that you copied form QC has ExternalIDField already populated. If it is not, then something is wrong with your configuration, for example, a wrong field type was chosen for the ExternalIDField.