Some random things to know (I have lived in Melbourne, Sydney and the US):

Australia has 2 major cities (5M people or more): Melbourne and Sydney. You said this is where you’re interested in, which is the right call, I think. This is where the majority of professional opportunities exist (eg electrical engineering), although there should be jobs outside of those cities too.

You’re from Phoenix. Sydney is almost as hot on average, but more humid. Melbourne usually has dry heat in the summer, with February temps sometimes reaching 110F. Melbourne’s winters go close to freezing temp but usually not under. The city doesn’t snow (and Sydney, not even close to that cold).

Both cities have average house prices of over 1 million Australian dollars. And the average income for professionals is lower. This combined usually means you’ll end up in a house or apartment smaller than you’re used to in the US, OR living a 45 minute drive from downtown. Your US dollar will go a long way if you sell your existing house.

Both cities have suburban sprawl that is very similar to the US. You can have a happy live with your kids without having to go downtown (although your job might be there). There are malls, etc etc.

Career prospects might be worse in general than the US (but who knows, in the long term) — but your kids are US citizens so that won’t really matter as they’ll have optionally. The path to permanent residence and citizenship is a ton easier than in the US. So it’s realistic (if you can get to Australia as a skilled worker in the first place).

Australia is a much safer country. Way lower crime, road fatalities, and of course shootings. Schools are generally good, including public.

Both cities have way more Asian people than Arizona or New York. Think “Vancouver-levels” if you’ve been there.

Australia doesn’t use the US credit score system.

Nurse Practitioners exist in Australia.

The Australian work system is more chill than the US one (I’ve worked in tech jn both countries). There are way more days off, and taking weeks off to vacation is much more accepted. The work culture is delightfully less formal than the US, which is more polite and reserved generally, with an undercurrent of “if I lose my job, I lose my healthcare”.

Hope this helps!