I don't have access to a hydrogen cylinder. Is it still possible for me to carry out this demonstration?

Yes. You can make hydrogen in the lab by reacting zinc with hydrochloric acid.

Do I need to use a fume cupboard for this demonstration?

No. This demonstration can be carried out in the laboratory without a fume cupboard but it would be wise to use safety screens between the apparatus and students. You always need to take care when making hydrogen because it forms explosive mixtures with air.

When would be the best time to show this demonstration?

You could use it in several ways. One possibility is to use it in the same lesson as a video of the Haber process so that students can make the link between what they observe in the demonstration and the reaction chamber in the video. Alternatively, the demonstration might be used as a 'starter' at the beginning of a lesson in which the theoretical background to the ammonia equilibrium is discussed.

I haven't carried out this experiment before, is it difficult to do?

As with any experiment that you haven't done before you need to practice it before demonstrating it to students. Showing it to another teacher is a good way of checking on the timings involved and making sure that the apparatus fits together. With a little practice you will find this demonstration is very straightforward.