I came to Qlik with no BI experience at all so I might be able to give you some advice. In theory, you could learn QlikView with nothing more than basic IT experience, using the various resources here in the Community, online blogs and videos and a whole lot of playing around. To make things easier a knowledge of managing data in databases would help with more complex data modelling. Experience with Excel or similar would help with expression building for charts and some knowledge around web/ux design would help your applications to work well and be appealing to use.
Obviously, Qlik provides training courses which might have their own pre-requisites and these can also provide a very rapid boost to your QlikView skills.
Most important is that you are motivated to do so. The program gives you satisfactory results after a short period of trial and error, which is also encouraging. So read some books (QV for developers e.g.), but most importantly try and fail. By failing yourself, you'll learn most.
