So me and my fiance both have our separate account and play on the same switch on the same island of course.
Now she is getting her own switch to play the game.

My question is if she deleted her account off the 1st switch the one we share would her character on the island just disappear and itll be my island then.

Or would the island entirely disappear and I would have to start a new island?

As long as you (tied to your account) are the representative your island will remain. Even with her account deleted you will still need to go delete her from the game (via the settings option on the title screen of the game). Otherwise it will leave her house, empty on the island.