If you are on firmware 5.1.1, well, that is one of the really early Kindle Touch firmwares. Like, really early.
Like, the Kindle Touch version of the Kindle 4 Non-Touch interface, which once again, is just embarrassingly early and has been completely revamped in a major, major way.
There is nothing wrong with it (or at least, no reason for us to think so), except for the fact that it hasn't been updated since it was originally built.
Please update it following the instructions here:
http://amzn.com/kindlesoftwareupdates/touch
You will then have the menu settings that we expected to see, which means you will have the Cover View setting you want.
There is no need to use Kubrick as knc1 suggested, since that would just get you the same version that you currently have (although it is useful for fixing damaged firmware, which again, we have no indication that that is the case). Or, technically, the minor patch version immediately after your current firmware, which is basically the same.