If you have QC and QTP installed on the same machine, there are two things you can do.
1) Click on Quality center connectivity icon in QTP located between OPTIONS and Object Repository. Complete the information about location of QC and stuff.and once you are done,after writing your script or recording, you can save it directly in QC
2) In QC go to the TEST PLAN module select a NEW TEST, on the right hand side pannel where you type design steps, there is a ICON for "Generating Script" between CALL a TEST and Insert Parameter to Generate SCRIPT, select QUICKTEST_TEST and record your script right into QC.
Hope this helps.
One of the basic idea for having QC is to be able to execute the test (QTP, WinRunner or any) centrally, and thereby better manage traceability, test case generation, execution and Defect logging.
Within TestLab you can run the tests from "Execution Grid" or "Execution Flow"