Shiken said:
Wouldn't a system to system transfer be able to bring the island over?

It works differently than cloud saves.

You can't do it unfortunately. I've also tried doing it because I want to transfer my save to another Switch but there is no even such option for AC. It is just not visible in the list of the games that support data transfer. So, until Nintendo implements some way to transfer saves, the only thing we can do is wait.