I don't think it is possible. I think you would not just need full QlikView, but I think you would need at least QlikView server. Personal edition is... well, personal. One user. Files cannot be shared. Someone may know better than me what the minimum setup for web distribution would be, though.
If it can be a static dashboard, you should be able to export images out of personal edition and put those images on the web. You could also export Excel files. Perhaps that would be sufficient, depending on your needs.
Depending on what you want to show and how you want to show it, you need a Server for sure, but the type of license and the number of users depends largely. I'd recommend you to check with your QlikTech sales rep, who may help you better knowing your requirements and your budget on how to get that done.
Personal Edition as John says above is just for your computer, unless you export data manually and use it in a different type of documents (powerpoints, PDFs, word documents and so).
Hope that helps.