Wacky idea. The EU is an awful lot of legislation to sign up to, not the most popular it's even been either. If it's just about trading space and resources for people I'd imagine a more bespoke arrangement would be preferable for both sides.
The four freedoms of the single market you get in return are incredible.
There are some joint institutions – for example, Food Standards Australia New Zealand (FSANZ), which is in charge of food regulation for both countries – but rather than an international bureaucracy, it is an Australian government agency. Even its Wellington office, all the employees are technically Australian public servants, even though they are mostly New Zealanders. New Zealand pays the Australian government part of FSANZ's budget; FSANZ issues new food regulations under Australian law and then the New Zealand government copies/pastes them into New Zealand law too: with rare exceptions, they are allowed to refuse to adopt a change if they disagree with it–Kava is a recent example, Australia has been cracking down on Kava due to concerns about the health risk, and using both controlled substances and food standards regulation to do so; New Zealand has been unwilling to go along due to its cultural importance to New Zealand's Pasifika (Pacific Islander) minority.
The issue is that the neighbouring countries are generally a lot poorer, and many of them are small island states, often with a shaky track record on democracy, so it just isn't politically and economically feasible to integrate them into the same economic relations as Australia and New Zealand have. There has been some talk of turning the Pacific Islands Forum, the regional international organisation, into a "Pacific Union", by expanding Australia/New Zealand's de facto economic union to the whole bloc. But realistically I think that's decades away, if it ever happens. And unless and until that happens, there is no real need to put the Australia/New Zealand economic union on a more formal footing.
We can send beer to your enemy in hopes they opt for boozing rather than shooting.
Also, they would like to sell things to and buy things from Germany and France, and the rest of the EU.
Economics determines military power. If Germany wants to build a military, they can and now they are, to a significant extent.
The EU parliament is elected and the EU council is indirectly elected.
A bureaucracy is a body of non-elected government officials (aka bureaucrats).
Trump-inspired conservatives are on their ways to be guaranteed majority at the next federal elections.
Canadians are just tired of Justin Trudeau after almost 10 years. Which happens to even the best of leaders, and JT is far from it.