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 a user table prior to the archive/restore.
Teradata suggests you take advantage of the Teradata Professional Services offering to set up standard DBQL rules and logging on your new system.