Wow! I've upgraded many Xerte installations many times over the years but never jumping so many versions in one go! I'm not sure any of us will have gone from 1.9 to 3.6 or even 3.x.
However unlike applications like Moodle etc there's no specific pre-requisite for upgrading to in-between versions. What I would suggest is that you need to liaise with your authors and schedule to do this when they have time to check/fix any LO's that are affected in any way. e.g. If you're still using 1.9 all the LO's will be viewed via Flash. Changing to 3.6 will include a huge number of changes since 1.9. Back everything up and possibly upgrade a test copy for your authors to check the impact on their existing projects.
Also if it's 1.9 does that mean it's sitting on a very old server with old OS/PHP/MySQL etc you could hit problems there too.
There is a guide to upgrading Xerte in the documentation folder.
HTH
Ron