Most estate agents are very short-term thinkers, it seems: they're response to a person contacting them from abroad is likely to be along the lines of "Once you're here we'll see what's around."

Perhaps you'd be better organising a short-term let (which is more expensive but which can be done from abroad) to start with. The cat will be in quarantine so that won't be an issue at first. Then you can look with a bit more time up your sleeve.

Definitely worth your husband contacting people at the UNSW: you never know what they might come up with.

Also, are there any flat/apartment-swapping organisations that you could tap into. I can't offer you any web addresses, I'm afraid, but this is a frequent source of accommodation for people going to or from the UK to Australia, so there might be something for Canada to Australia as well. It is particularly commonly used here by academics.