The only sure way to get Fauna in Animal Crossing New Horizons is by getting her Amiibo card and using it to invite her to your campsite. If you can't get your hands on her amiibo then you'll need luck and persistence. The most you can do is visit mystery islands when you have an empty lot on your island. There's no telling how many islands it'll take to find her so you'll need to save up some Nook Miles, then take the time to buy Nook Miles Tickets and visit Mystery Islands until you find her. Another option is hoping Fauna shows up at your campsite and when she does don't stop talking to her and playing games with her until she agrees to move to your island.