No, it is not going to be possible to use our Web Part in SharePoint Online, the Web Part is only supported through SharePoint 2010. There is a new method of doing things for SharePoint 2013 etc., which is documented in the Workbench manual. Section 8.6 QlikView Integration with SharePoint 2013 should be what you are looking for in the way of documentation on how to do things. I am not certain this will work with Online, but it would be your best shot at a possible working solution.
The Workbench manual is included in the QlikView_DocumentationAndTutorial_Complete_Setup.exe on the download site to which I hope you have access, but if not, you may always contact support and request the Tech to email you a copy. The other key thing I wanted to mention here is that your QlikView Server license will need to have the Workbench parameter in the License Enabler File (LEF), which you can see via the QlikView Management Console -> System -> Licenses -> QlikView Server -> QlikView Server License tab. What you want to confirm is there is the following line: