Bring a town over from Dolphin

It is a normal memory card file

Animal Crossing writes its town to a GameCube memory card, and a .gci is one of those files taken off the card. Dolphin writes them, real hardware writes them, and this reads and writes the same thing. Your town inside it is never repacked.

Australian and European saves work too. They differ from a US save only in a short release code at the start of the file. Importing one changes that code to the US one, and Export a copy writes the code of the disc you are playing with. To take a town back to an Australian or European game, export it while playing with that disc.

Moving a town in

In Dolphin, open the memory card manager and export the Animal Crossing save to a .gci file.

Here, open the Play page, click the save status in the top bar to open the save options, and choose Import a save file. Pick the .gci and your town loads.

Taking one back out

Same panel, Export a copy, and you get a .gci on your computer. Import it into Dolphin or onto a memory card for the same version of the game as the disc you play with here, or keep it as a backup.

Worth doing either way. Your town lives in your browser's storage, and clearing site data would take it with everything else.

Or skip the file entirely

Signing in turns on cloud saves, and your town follows you to any device you log in on. The .gci route is for bringing an existing town in, or for keeping a copy somewhere we are not.