You are correct that the detail number is not maintained in Quik History, nor is the batch/entry number maintained in Quik Invoice. Therefore, neither is available to be reported on.
The linking of QH to QI in Quik Reports can only be done by Customer Number or Acct/Dept, not by document number or line number. I don't think that Report Master would be able to make this relationship either; you would have to have a virtual link Document/Entry/Detail, and there is no Entry field available.