Did you read TFA (the Reuters one) that quotes the Australian trade minister? Or are you somehow more involved in determining trade agreements than the minister?

Trump has upended decades of stable trade relationships. I would not assume anything right now.

(To be clear, neither Canada nor Australia are claimed to be seeking to be EU members - but closer trade ties with the EU appear to be on the cards for both nations. When you can no longer trust the US to act in good faith, everything changes.)

I suspect it'll be expanding the current trading agreement to allow more direct investment. Canada and Australia both have lots of raw materials the EU needs. I suspect you'll see more types of worker visas (similar to the old NAFTA T1 styles that allow relatively easy sponsorship of employees).

I'd love to have full rights to live and work in the EU, but I'd be happy just being able to visit the EU as a Canadian and use the EU customs lines. I don't think Canada would go for full mobility. We're just now dealing with the backlash of too many immigrants from South Asia, a "flood" of poorer Eastern Europeans would probably rekindle that.