I had the same idea, and I see that you haven’t yet received a reply. Here’s what I know:
There shouldn’t be much problem connecting your Ring cam to a WiFi network in another country, but be aware that different countries have different rules about what WiFi bands are allowed to be used, and your Australia cam might not conform to your vacation country’s band requirements. It shouldn’t generate any signals on bands that it’s not using, since it’s a client device, so, technically, you wouldn’t be violating any rules. But it’s possible that your cam might not see the WiFi network at your AirBNB. But the odds are that it will work.
The next issue, and the one that I’m wondering about, is whether you can have a Ring account with more than one “home address”, or whether you can have Ring devices at different addresses on the same account. I haven’t figured this out, yet, but I’m sure there’s a way to do it.
Regarding privacy and such, laws vary greatly in different countries. In some places, no one is allowed to enter your rental property without warning and/or permission. But AirBNB has its own rules about security cameras, found here:
In the section “Rules for guests”, you will find the following:
“Our policy prohibits the use of a security camera or any other recording device by a guest to monitor a host or any third party present in the listing without the consent of that person.”
That’s all I know at the moment.