What if Canada and Australia had a relationship that like EU countries have?

Hi!

Canadian here.

So there's some talk up here about Canada needing a new trading partner, and my mind immediately goes to Australia. With Canada's richness in water and oil, and Australia's richness in minerals. But I'd like to take the thought a step further. With a similar population density, language, and even monarchy. What if we formed a relationship similar to that of what EU countries have between each other?

I grew up near Whistler Canada, and its already kind of like an Australian/New Zealander home away from home and though I've never been to Australia, the thought having somewhere warm that I could go and work honestly seems awesome to me. It also seems like a fair way for both countries to diversify their economies. Yes there are exchange programs however they favor those under 30 years old, Why be ageist about it?

Anyways Australians (and New Zealanders), what are your thoughts?

And may the polar bears Canada, and kangaroos Australia and sheep of New Zealand go about their happy days :)