I think the most full proof supply chain might be the internet, I don't think shipping to the UAE would be a big deal for a big retailer like amazon, there may be some extra international shipping costs. Some of the chichilla supply vendors around the internet might not mind sending there either but it is certainly worth doing some up front research, your chinchilla is lucky to have such a sweet and thoughtful owner.
Some other things to consider is your length of stay in Dubai and the heat. If you are only going to be in Dubai for a year and then back to Canada keep in mind to understand Canada's laws as well because the chinchilla will need to cross another border. Maybe since the chinchilla was already there you can obtain some reimport exemptions and things like that. Dubai is a very desert like climate so be sure your living quarters will have some full proof AC. Temps of 41.3 degrees C is an average high in August
Wishing you the best of luck. Sorry to fill your head with all these ideas, its just that I already did a lot of research because I almost moved internationally one time.