Is there anything to do while waiting for results of a thesis examination?
From reading the examination instructions it appears that if I get my degree, it could be between 6 weeks to a year.


Have you talked with your advisor about the time frame you should expect?  University policies often allow for a wide range of possible schedules, to account for differing circumstances.  The advisor generally has a clear idea of which part of the range a student is likely to end up in (although of course there are no guarantees).

When you reach the point of graduating, there should be little uncertainty left about the quality or value of your work, because your advisor should have been offering feedback and guidance along the way.  If your advisor is genuinely unable to predict whether it will be closer to 1.5 or 12 months more, then it is a worrisome sign (suggesting inexperience or negligence on the advisor's part, or that they suspect something may be wrong with your dissertation).  


  Considering the time-frame is so variable, is there anything else I should be doing or planning?


I agree with the comments above about job applications.  In the cases I am familiar with (mathematics in the U.S.), academic job applications are due around December, which is typically about six months before graduation occurs.  This includes both faculty and postdoc applications.  Practices may differ in other fields or countries, but it's almost always a good idea to begin looking substantially before you actually graduate.