Database Query Logging (DBQL) data is not archived or restored, with the exception of the DBQLRuleTbl and DBQLRuleCountTbl which are archived/restored as part of database DBC.
If you want to migrate the DBQL logging data to the new system the data must be copied from the DBQL tables to user tables prior to the archive/restore.
Teradata suggests you take advantage of the Teradata Support offering to set up standard DBQL rules and logging on your new system.