To the best of my understanding I know that during WW1 Britain still controlled their foreign affairs and so were responsible for declaration of wars. By the time WW2 began however Canada and Australia were completely independent so why did they join the war so quickly and not stay neutral as Ireland did?
I can't speak to Australia but Canada in WW2 was a Dominion of the British Commonwealth. While it's an independent country, it still has close ties with UK itself. It wasn't until 1982 that British Parliament approval were required to make certain amendments to the Canadian constitution.
Ireland on the other hand became an independent sovereign republic as of 1922 with no ties to UK.
Australia considered it's interests and identity to be inextricably linked to Britain's.
On being informed by the U.K. that her government intended to fulfil Great Britain's obligations to Poland and was convening Parliament on 24th August 1939 to seek wide emergency powers, the Australian Cabinet met on 24th August and prepared recommendations for war legislation under the Defence Act, and issued preparatory instructions to the Navy, Army and Air Force.
On the 25th August the Australian Prime Minister made a public broadcast explaining the situation in Europe to the Australian people and saying "The next few hours may find the world at war. We in Australia are involved,because, in plain English, the destruction or defeat of Great Britain would be the destruction or defeat of the British Empire and would leave us with a precarious tenure of our own independence"
On 1st Sep 1939 Australia heard that German troops had entered Poland and bombed Polish cities and on 3 Sep on receiving confirmation of Britain's declaration of war on that date, the Australian government also declared war.
The Prime Minister's broadcast to the Australian people started out "It is my melancholy duty to inform you officially that, in consequence of a persistence by Germany in her invasion of Poland, Great Britain has declared war upon her and that, as a result, Australia is also at war."
TLDR Although independent, Australia in 1939 identified its cultural identity and national interests so closely with Britain and the Empire that there was no real consideration that she wouldn't support her in war
Reference: Australia in the War of 1939-45 Official History, Australian War Memorial