Yes Stephen, you are quite right, I do forget that a lot of organizations using Moodle are corporate or commercial based. Please accept my apologies, and this suggestion:
The transition from Moodle 1.9 to v2.x cannot be accomplished easily when you have no opportuntity to make the kind of clean breaks discussed earlier. This then makes it essential to apply some planning to the process. Whatever is done, I suggest you set up a v2.2 and make sure you have all your courses in it before you do anything else.
It can be done quickly, that is, select a date in the future, prepare a Moodle 2.x and parallel it with your existing v1.9.x, that is, make sure it has all the same courses and users all set up and on that date, everyone moves over on one day.
Alternatively, once you have a v2.x setup, start all new enrollees in it while existing enrollees complete their current courses in the v1.9.x.
The drawback in the first instance is that it is possible that people will lose their work, their grades from gradebook, their history, which is not really acceptable. It means you have to make sure you have these things properly recorded and available to them if needed. The drawback in the second instance is that you have to make sure that your tutors, teachers, facilitators, mentors etc., can work in both Moodles and that you have sufficient server space to make it all work.
This can be a starting point, if you have not already considered it.
Of course, there is another method for making the transition while live, well almost. First, create a test Moodle of v1.9.x exactly the same as your production site, complete with user files and everything. Use the upgrade process to trial doing it (you can find more information about upgrading to v2.1 here). Repeat it several times if needed. When you are confident you can do it without a lot of fuss, repeat the process in your production site. Alert everyone that at 12:00 midnight on the 1/4 you are going to take your site offline. You can then place the site into Maintenance mode at that time, confident that no-one will be online. Do your upgrade and if you do not have non-standard blocks or filters or plugins, it should just upgrade easily. Make sure you have the right version of PHP and database server and everything...