Can QAP launch an application with administrator privileges?

Yes. If QAP is running with administrator permission, all applications it will launch will automatically inherit the admin level. Is it a good idea to launch QAP as Administrator? This could allow the launched applications to do changes on your system without prompting you. From a system security point of view, this may put your system at risk. In other words, you have to know what you are doing.

If QAP is running with normal user privileges, you can launch only some favorite applications with elevated privileges. Check the option Elevate application with administration privileges in the Advanced Settings of the Edit Favorite dialog box. Of course, before launching the application, Windows will display the usual approval dialog box or ask for the admin password.

See more information about Windows ACL (Access Control List) and QAP.